1 00:00:18,010 --> 00:00:23,360 Hello, this is a continuation of previous session Risk and Return, where you discussed 2 00:00:23,360 --> 00:00:28,279 about the estimation of return for different securities, expected as well as historical 3 00:00:28,279 --> 00:00:35,279 rate of return. Then you talked about the risk involved in the investment security assets 4 00:00:35,410 --> 00:00:40,090 and different factors that contributory risk and how do we measure the risk in terms of 5 00:00:40,090 --> 00:00:42,870 standard deviation, ranges, variance and all those measures. 6 00:00:42,870 --> 00:00:47,900 This is a continuation of the previous lecture, in this we are going to talk about the concept 7 00:00:47,900 --> 00:00:51,909 of required rate of return, what are the factors that affect as well as you can talk about 8 00:00:51,909 --> 00:00:56,220 the portfolio risk and return. When we say portfolio, it is a combination of different 9 00:00:56,220 --> 00:01:02,030 financial assets and in this portfolio risk, return depends upon obviously, the individual 10 00:01:02,030 --> 00:01:06,860 asset that is comprising of the portfolio comprises of. 11 00:01:06,860 --> 00:01:12,620 So, coming to the first one, that is concept of required rate of return we it is nothing 12 00:01:12,620 --> 00:01:18,680 but the rate of return expected by the investor from an investment. And the factors that affect 13 00:01:18,680 --> 00:01:23,830 the required rate of return could be we have the time value of money, time value of money 14 00:01:23,830 --> 00:01:30,330 is something a simple principle. When we say that today’s 1 rupee is not 15 00:01:30,330 --> 00:01:35,800 same as tomorrow’s 1 rupee, if somebody is investing some x rupees today, obviously 16 00:01:35,800 --> 00:01:40,850 will be expecting something more tomorrow. It is because, if he is investing in an asset 17 00:01:40,850 --> 00:01:46,140 today, he is just differing the conception of his whatever he wants to consume today, 18 00:01:46,140 --> 00:01:50,960 he is going to offering to tomorrow. So, for that he needs a reward and in that 19 00:01:50,960 --> 00:01:55,910 case, he should be getting that much money where he can consume little more than what 20 00:01:55,910 --> 00:02:01,010 he is scarifying today. So, because of you have a time value of money is one of the basic 21 00:02:01,010 --> 00:02:07,350 fundamental principle in an investment scenario, because we invest today to get something back 22 00:02:07,350 --> 00:02:13,760 in future. So, there is a time gap and people will like to have a reward for waiting or 23 00:02:13,760 --> 00:02:20,190 with holding conception with that resource that they have contributed to by an investment. 24 00:02:20,190 --> 00:02:27,190 Next thing that we have is the expected rate of inflation besides the change in preference, 25 00:02:28,700 --> 00:02:33,549 change in conception, differing the conception to future we will also have something like 26 00:02:33,549 --> 00:02:39,359 expected rate of inflation; that means, if today I am able to buy 10 units of products 27 00:02:39,359 --> 00:02:45,620 with 100 rupees of currency and tomorrow I may not be able to buy the same 10 units of 28 00:02:45,620 --> 00:02:49,590 products, I may be able to buy may be 9 or 8 units of product because there is a there 29 00:02:49,590 --> 00:02:52,909 could be change in the price level of the product that I am buying. 30 00:02:52,909 --> 00:02:58,090 So, in that case there is an inflation that is going to take place, say that inflation 31 00:02:58,090 --> 00:03:01,590 also will be affecting the required rate of return, if the expected inflation is going 32 00:03:01,590 --> 00:03:05,989 to be 5 percent, the required return could be x, if it is going to be more than 5 percent, 33 00:03:05,989 --> 00:03:09,359 the inflation is going to more than 5 percent, then required rate of return is going to be 34 00:03:09,359 --> 00:03:13,989 more than that. So, in that case inflation is one thing which 35 00:03:13,989 --> 00:03:20,609 has to be captured as a factor of affecting the required rate of return, then we have 36 00:03:20,609 --> 00:03:27,069 the risk involved; risk as you discussed previously. So, if there is a high risk involved and then 37 00:03:27,069 --> 00:03:30,569 obviously, I will be expect more risk rate of return, if the low risk involved, I will 38 00:03:30,569 --> 00:03:34,779 have more rate of I will be expect more rate of return and when it as say there is no risk 39 00:03:34,779 --> 00:03:40,209 involved, there is no uncertainty when about what I am going to get back from the investment. 40 00:03:40,209 --> 00:03:45,559 In that case, my required rate return will be equal to the will be only taking care of 41 00:03:45,559 --> 00:03:50,150 my time value of money as well as the rate of inflation in the economy or what are the 42 00:03:50,150 --> 00:03:51,189 sector for that matter. 43 00:03:51,189 --> 00:03:57,779 So, risk involved as we discussed previously, risk involved could be of different types 44 00:03:57,779 --> 00:04:03,290 and like business risk, financial risk, country risk, exchange rate risk. Before you go further, 45 00:04:03,290 --> 00:04:07,889 we may go to one another concept called a real risk free rate of return that is called 46 00:04:07,889 --> 00:04:11,199 RRFR. In the real risk free rate of return is the 47 00:04:11,199 --> 00:04:18,199 thing, where we say there is no inflation; that means, if there is going to be 7 percent 48 00:04:20,290 --> 00:04:24,639 inflation and there is a rate of return is let us say expected is 12 percent; that means, 49 00:04:24,639 --> 00:04:28,060 real could be 12 minus 7 in a 5 in a very simpler term. 50 00:04:28,060 --> 00:04:34,790 But the formula is not that simpler, as this is little bit complex little and in the real 51 00:04:34,790 --> 00:04:38,630 risk free return real risk free rate, what we assume is there is no uncertainty about 52 00:04:38,630 --> 00:04:43,240 future cash flow, there is no inflation and we do not say that there is going to be any 53 00:04:43,240 --> 00:04:48,190 fluctuation in what we are going to get and one when we say future cash flow, if it in 54 00:04:48,190 --> 00:04:52,300 the case of a debenture bond, the future cash flow is determinant in terms of the interest 55 00:04:52,300 --> 00:04:56,240 received and then we also get something back in terms of principle. 56 00:04:56,240 --> 00:05:00,900 So, there is no uncertainty as well as in terms of interest to be received as well as 57 00:05:00,900 --> 00:05:05,020 in terms of the principle, I am going to get back. So, there is similarly in an equity 58 00:05:05,020 --> 00:05:08,440 share, I do not have any uncertainty about getting something dividend, I also do not 59 00:05:08,440 --> 00:05:14,400 have any uncertainty about getting some change in the market price. So, if that is not there 60 00:05:14,400 --> 00:05:20,280 then, we say there is no uncertainty and then only the inflation is not captured also. 61 00:05:20,280 --> 00:05:24,660 So, in that case the real risk free rate of rate is defined whether, there is no inflation 62 00:05:24,660 --> 00:05:31,560 and there is no uncertainty about the future cash flow. Then also it is also only influenced 63 00:05:31,560 --> 00:05:35,300 by the time preference for consumption of income and investment opportunities in the 64 00:05:35,300 --> 00:05:40,220 economy. So, I will withhold the consumption till tomorrow. 65 00:05:40,220 --> 00:05:44,820 So, only for that I will like to have some reward, I do not bother at inflation because, 66 00:05:44,820 --> 00:05:49,550 the inflation is absolutely 0 in this case. I do not bother about these changes in the 67 00:05:49,550 --> 00:05:53,920 price level, I do not bother about the future cash flow, it is going to come because that 68 00:05:53,920 --> 00:05:59,000 is going to come all of certainty. So, only thing that I am going to capture 69 00:05:59,000 --> 00:06:04,050 in my expected rate of return which is my risk free also, is the only that I am with 70 00:06:04,050 --> 00:06:08,110 holding my consumption till tomorrow. So, depending on the economic condition, I am 71 00:06:08,110 --> 00:06:12,560 expecting something going to better happen then on that case, I can expect that I will 72 00:06:12,560 --> 00:06:15,170 consume tomorrow, so I can invest today. 73 00:06:15,170 --> 00:06:21,430 So, to whatever is return I am expected, reward that phenomenon that is called my risk, real 74 00:06:21,430 --> 00:06:28,140 risk free rate. And there is simpler formula here, where we say real RFR is nothing but 75 00:06:28,140 --> 00:06:34,440 1 plus in the numerator, we have 1 plus nominal RFR and then you have got 1 plus rate of inflation. 76 00:06:34,440 --> 00:06:41,440 That means, if we have if you have nominal RFR is let us say 0.12 and the rate of inflation is 0.05, where that is called 77 00:07:03,340 --> 00:07:10,340 5 percent then my real RFR will be solve like this, it will be 1 plus 0.12 divided by 1 78 00:07:14,510 --> 00:07:21,510 plus 0.05 minus 1. So, that is nothing but 1.12 divided by 1.05 minus 1. So, this is 79 00:07:23,020 --> 00:07:28,650 the way one can get the real rate of return which will obviously, between something between 80 00:07:28,650 --> 00:07:33,160 5.12 percent if you calculate further. 81 00:07:33,160 --> 00:07:37,640 Then similarly, we can also find out what is the nominal risk-free rate return, which 82 00:07:37,640 --> 00:07:43,090 will depend upon the condition in the capital market. That means, if the condition in capital 83 00:07:43,090 --> 00:07:49,460 market is going to be good, then that case I am going to have more, I will expect little 84 00:07:49,460 --> 00:07:55,200 more rate of return because the condition is good and as because the economy is going 85 00:07:55,200 --> 00:07:59,600 to invest in good assets and the assets are going to give you good return in future. 86 00:07:59,600 --> 00:08:05,630 So, for that matter, I will expect a high rate of return as such, then we have one more 87 00:08:05,630 --> 00:08:10,920 thing that is expect rate of inflation. So, inflation is going to be higher, then I will 88 00:08:10,920 --> 00:08:17,210 expect more rate of return in nominal form and next thing that if you look at if you 89 00:08:17,210 --> 00:08:22,600 change the formula, then 1 plus real RFR into 1 plus expected rate of inflation minus 1 90 00:08:22,600 --> 00:08:28,670 gives this one. So, coming back to this particular point, if you get these as x, if you calculate 91 00:08:28,670 --> 00:08:35,670 that means, we can go to nominal RFR by applying the formula that is 1 plus x into 1.05 minus 92 00:08:41,779 --> 00:08:44,339 1. So, the same formula has been derived out 93 00:08:44,339 --> 00:08:48,260 of the previous formula here and the nominal is nothing but so that means, you have the 94 00:08:48,260 --> 00:08:53,950 real rate of return expected and you has the also the inflation rate multiply that and 95 00:08:53,950 --> 00:09:00,510 minus 1, whatever that we get that is called the real say nominal rate of risk free rate 96 00:09:00,510 --> 00:09:04,320 of return. Obviously, in this case it is going to be 0.12 because if you have use this same 97 00:09:04,320 --> 00:09:10,520 input, which is used in the previous example. 98 00:09:10,520 --> 00:09:17,520 Then next thing is that what is the risk that is affecting is a continuation of the previous 99 00:09:19,750 --> 00:09:25,510 class also, what is the risk that is there which will be affecting the business. So, 100 00:09:25,510 --> 00:09:30,300 one is called the business risk, business risk means the company for whatever assets 101 00:09:30,300 --> 00:09:34,180 they have put where with that, where the revenue coming from which type of sector they are 102 00:09:34,180 --> 00:09:37,400 operating in. So, and what is the cost structure of the 103 00:09:37,400 --> 00:09:42,100 particular company? The cost structure of the company is more in terms of fixed cost 104 00:09:42,100 --> 00:09:45,640 and less in terms of variable cost then, they will have to go for a higher production and 105 00:09:45,640 --> 00:09:48,860 sales level; so that they can recover and they can break of in point. 106 00:09:48,860 --> 00:09:53,880 They can they can think of having some profit. So, the risk is obviously going to be higher, 107 00:09:53,880 --> 00:09:57,830 if the company relatively having a high fix cost. So, this something also known as operating 108 00:09:57,830 --> 00:10:02,260 risk and similarly company might have been to gone to different business assets. So, 109 00:10:02,260 --> 00:10:04,740 that is also going to affect the business risk of the company. 110 00:10:04,740 --> 00:10:09,700 So, if the investor feels that the business risk is higher in this company, so obviously, 111 00:10:09,700 --> 00:10:16,260 in that case, expect rate return which captures the risk in that will be higher, then next 112 00:10:16,260 --> 00:10:23,260 in that we have is the financial risk. Financial risk comprises of the fact that, the company 113 00:10:24,190 --> 00:10:30,839 has borrowed money and investing. So, if there is any profit, any cash flow before we take 114 00:10:30,839 --> 00:10:35,120 care of other operating expenses, we have to take care of the interest obligation and 115 00:10:35,120 --> 00:10:39,610 also you have to take of the principle repayment. So, there is a claim of the creators over 116 00:10:39,610 --> 00:10:45,170 that if it is a bad condition or good condition and if there is a profit making or loss making, 117 00:10:45,170 --> 00:10:50,430 whether you have surplus or not interest has to be paid. So, in a very bad condition, interest 118 00:10:50,430 --> 00:10:54,720 has to be paid in that case, the return that is available for the cash flow available, 119 00:10:54,720 --> 00:10:59,070 for equity investors becomes very less. Similarly, if there is a good condition in 120 00:10:59,070 --> 00:11:04,550 the market, good sales is taking place for this company the target company in that case; 121 00:11:04,550 --> 00:11:08,200 obviously, the company is not going to pay more interest because the company is doing 122 00:11:08,200 --> 00:11:11,740 well, company will pay the same commutative rate of interest could be 10 percent, 12 percent 123 00:11:11,740 --> 00:11:16,010 whatever on the date that the company has taken from the market or from the financial 124 00:11:16,010 --> 00:11:19,440 institution. So, in whatever the interest is something 125 00:11:19,440 --> 00:11:23,990 like a fixed obligation, which has to be honored irrespective of the circumstance. So, high 126 00:11:23,990 --> 00:11:29,110 date will lead to high interest, high date inflation to equity is going to be more risky 127 00:11:29,110 --> 00:11:33,240 than any other company which has got less date to equity. So, the company that way I 128 00:11:33,240 --> 00:11:38,060 am investing, if they have got more exposit date inflation to the equity that company 129 00:11:38,060 --> 00:11:43,330 is going to be riskier than the rest of the company or the industry as such. So, that 130 00:11:43,330 --> 00:11:47,730 is called financial risk next that we have is called liquidity risk. 131 00:11:47,730 --> 00:11:52,470 Liquidity risk is something where we have a doubt that, whether what have we invested 132 00:11:52,470 --> 00:11:59,470 today in the market can I get it get out of or not out of the same or not, because a typical 133 00:11:59,670 --> 00:12:03,820 concept of market, where the best concept of market could be that, when one of the best 134 00:12:03,820 --> 00:12:07,660 condition of the market is that, you should have an easy entrance easy exit option. 135 00:12:07,660 --> 00:12:12,410 It should not be that, I invest in a particular security and then I will like to come out 136 00:12:12,410 --> 00:12:16,630 of that for whatever is in and there is no avenue for me to come out; that means, possibly 137 00:12:16,630 --> 00:12:20,460 there is no buyer of that particular security or I do not know where to go and sell this 138 00:12:20,460 --> 00:12:25,399 security so that, I can get back my money. So, that is one, similarly if I have I have 139 00:12:25,399 --> 00:12:28,880 miss to invest when the company is should this particular security, now I feel that 140 00:12:28,880 --> 00:12:33,399 particular investment attractive for me, I should have an option to invest in that particular 141 00:12:33,399 --> 00:12:37,010 security. So, I cannot do that in one case, the company 142 00:12:37,010 --> 00:12:41,960 issues additionally those securities in future course of time, but I need not wait for that, 143 00:12:41,960 --> 00:12:47,339 if that particular investment is showed by the existing investor - investment holder 144 00:12:47,339 --> 00:12:51,589 in that case I can also buy. So, this is something called the provision of liquidity in the market, 145 00:12:51,589 --> 00:12:57,529 where you can buy and sale the shears or bonds or debenture or whatever financial assets 146 00:12:57,529 --> 00:13:01,860 that you are holding. So, you should not have to wait for some more time to find out who 147 00:13:01,860 --> 00:13:06,310 can buy the share. Say if I feel that who are have invested there 148 00:13:06,310 --> 00:13:12,040 is a problem in liquidity in that particular investment to cash are transparent to someone 149 00:13:12,040 --> 00:13:16,410 else, there is no readymade market for that then; obviously, I am thinking there is a 150 00:13:16,410 --> 00:13:21,410 risk involved as well liquidity is concerned. So, stock exchanges or any exchange financial 151 00:13:21,410 --> 00:13:25,089 exchange which is going to facilitate this particular function that is, when you are 152 00:13:25,089 --> 00:13:28,430 going to buy and sale this security. So, if you have already bought this security you 153 00:13:28,430 --> 00:13:33,339 can as well sale it and get the cash back, if you have not got it you can as well buy 154 00:13:33,339 --> 00:13:39,040 that security from the secondary market. So, that is what the liquidity is, I am presuming 155 00:13:39,040 --> 00:13:43,390 the investors presume that liquid is there or not there accordingly the risk case to 156 00:13:43,390 --> 00:13:48,020 be incorporated. Then we have got something called exchange rate risk. 157 00:13:48,020 --> 00:13:53,120 Exchange rate risk could one way that the company is investing into certain assets, 158 00:13:53,120 --> 00:13:58,209 certain raw material, they are consuming which may depend upon for x rate because they are 159 00:13:58,209 --> 00:14:02,330 importing such items. Another exchange rate could be that company’s sales itself takes 160 00:14:02,330 --> 00:14:07,750 place outside, though they are sourcing and producing everything and the domestic market, 161 00:14:07,750 --> 00:14:11,180 but they are selling most of the items in the foreign market. 162 00:14:11,180 --> 00:14:14,860 So in that case, obviously, the realization from the sales would depend upon the change 163 00:14:14,860 --> 00:14:20,860 in the for x rate dollar to rupee or pounds turning to rupee or euro to rupee, that rate 164 00:14:20,860 --> 00:14:25,430 will going to affect the sales level; if the quantity may remain same, but the value of 165 00:14:25,430 --> 00:14:29,170 the sales may go up or decline because of the change in the for x rate. 166 00:14:29,170 --> 00:14:34,540 Another exchange rate is that is risk is that, as an investor I may like to invest in a company 167 00:14:34,540 --> 00:14:40,880 which is in Japan or Europe or US or Canada for that matter. So, in that case my investment 168 00:14:40,880 --> 00:14:47,420 return and everything will depend upon for an x as rate condition between that country 169 00:14:47,420 --> 00:14:52,310 where I am investing and the country which I would belong to. So, that is also going 170 00:14:52,310 --> 00:14:56,399 to be there, so the exchange rate risk is also going to be captured as a part of risk 171 00:14:56,399 --> 00:15:00,760 and if the exchange rate risk is preserved by the investor then obviously, return expected 172 00:15:00,760 --> 00:15:07,089 by the investor is going to be more. Coming to the next one, that you have a something 173 00:15:07,089 --> 00:15:13,250 call country risk. So, I have beside the fluctuation for x rate, the country that I am going to 174 00:15:13,250 --> 00:15:17,470 invest even if the both the countries, where I can exchange my I can buy the asset in a 175 00:15:17,470 --> 00:15:21,430 particular currency in both the countries, but still one country may be more riskier 176 00:15:21,430 --> 00:15:25,140 to invest than another country because of the political and economy condition in that. 177 00:15:25,140 --> 00:15:29,339 If there is some political unrest in that particular country or the democratic set up 178 00:15:29,339 --> 00:15:36,339 is not that well-functioning, in that case and there is no proper legal law and all mechanism 179 00:15:36,550 --> 00:15:41,520 where you can resolve your disputes and everything. So, if such things the governing condition 180 00:15:41,520 --> 00:15:45,550 is not good in that country, obviously that country is going to be high risk than the 181 00:15:45,550 --> 00:15:50,410 other country, where these conditions are well set and you do have a good mechanism 182 00:15:50,410 --> 00:15:56,300 of governance as well as redressing your the disputes and whatever. 183 00:15:56,300 --> 00:15:59,990 So in that case, the country risk is going to be lower. So, I am also going to capture 184 00:15:59,990 --> 00:16:03,680 the industries also going to capture the country risk as a part of risk, when the investor 185 00:16:03,680 --> 00:16:10,680 is investing in a particular security, particularly when this security is that belongs to a company 186 00:16:10,680 --> 00:16:15,000 which is established and operating in another outside country as such. 187 00:16:15,000 --> 00:16:21,500 So, these are the different risk that is there in the market. So, the risk premium becomes 188 00:16:21,500 --> 00:16:27,750 essentially a function of business risk, financial risk, liquidity risk, exchange rate risk, 189 00:16:27,750 --> 00:16:33,089 country risk. And all these risks which are there, the conditions the risk is there, these 190 00:16:33,089 --> 00:16:39,459 risk are typically market specific risk. So, business risk, but for the risk involved 191 00:16:39,459 --> 00:16:46,459 in the cost structure the company, these are the risks which somebody cannot mitigate on 192 00:16:47,470 --> 00:16:51,690 it is own. So, it is something like a market risk, which is called as systematic market 193 00:16:51,690 --> 00:16:56,260 risk. Systematic market risk means, the risk that is involved in investing particular asset 194 00:16:56,260 --> 00:17:00,950 which cannot be diversified by investing another security. 195 00:17:00,950 --> 00:17:06,350 So, these risks are going to continue on whether I change the investment from x to y or y to 196 00:17:06,350 --> 00:17:11,539 z for that matter. So, this is called systematic markets which you cannot diversify; what you 197 00:17:11,539 --> 00:17:15,890 can diversify only on a systematic risk, which is unique to the particular company where 198 00:17:15,890 --> 00:17:16,970 I am investing. 199 00:17:16,970 --> 00:17:22,770 So, the risk premium depends upon the systematic risk of the… or the market risk for that 200 00:17:22,770 --> 00:17:29,770 matter. Now having discussed the risk premium assets, there is a relation between risk premium 201 00:17:30,730 --> 00:17:35,900 and the portfolio theory. Portfolio theory in detailed we will be discussing in subsequent 202 00:17:35,900 --> 00:17:39,559 classes and even you talking about portfolio theory. 203 00:17:39,559 --> 00:17:44,000 But typically when you say portfolio nothing but the combination of financial asset the 204 00:17:44,000 --> 00:17:51,000 particular investor is owning or investing in. So, in that coming to that, relevant risk 205 00:17:51,410 --> 00:17:56,150 measure for an individual asset is the co-movement with the market portfolio. 206 00:17:56,150 --> 00:18:01,520 So, when you talk about portfolio theory context, what he say here is that whatever when you 207 00:18:01,520 --> 00:18:07,179 talking about individual asset, how this particular asset is moving with another in the market 208 00:18:07,179 --> 00:18:13,270 asset. So, moving with the market means, if the market is going up then this particular 209 00:18:13,270 --> 00:18:16,780 securities also going up; the market gives a positive return this could also gives a 210 00:18:16,780 --> 00:18:21,730 positive return, market gives a negative return this could market also gives a negative return. 211 00:18:21,730 --> 00:18:27,090 So, it may be so that, that is the particular security is moving and tandem with the market 212 00:18:27,090 --> 00:18:31,370 asset, but there may be some security which may move against the market, against means 213 00:18:31,370 --> 00:18:36,170 the market is actually upward and this particular stock is actually moving downward. 214 00:18:36,170 --> 00:18:42,410 So, there is an expected fall in the market represent by the index like sensex or nifty 215 00:18:42,410 --> 00:18:48,950 or nasdaq index s n p nadac index. So, I like to buy the share of that company which is 216 00:18:48,950 --> 00:18:53,250 going to actually move upward direction, when the market is down. So, that is called that 217 00:18:53,250 --> 00:18:58,840 is moving in opposite direction in the market. So, any share can move in either opposite 218 00:18:58,840 --> 00:19:02,650 direction or in the same direction in the market or may not follow a particular path 219 00:19:02,650 --> 00:19:06,270 like this direct or indirect path, it may follow it own path. 220 00:19:06,270 --> 00:19:11,240 So, this measure that we talk about the how the particular stock is moving along with 221 00:19:11,240 --> 00:19:17,390 the market portfolio. Market portfolio is typically comprising of the ideally market 222 00:19:17,390 --> 00:19:21,929 portfolio should comprise of all the assets all the financial assets traded in the market 223 00:19:21,929 --> 00:19:28,929 whereas, but it is not possible to find out the portfolio of the assets of all the investments 224 00:19:29,410 --> 00:19:32,830 in the market assets. Because some of the investments may not be 225 00:19:32,830 --> 00:19:38,020 traded may not be total liquid highly liquid for that matter. So, you do not get the proper 226 00:19:38,020 --> 00:19:43,910 price return statistics on those. So, we rather go for a representative market portfolio, 227 00:19:43,910 --> 00:19:49,350 that is could be an index. So, best of index could be the one of this bse sensex or nasdaq 228 00:19:49,350 --> 00:19:54,840 index or standard and poor's index or we have about cns nifty in indian context. 229 00:19:54,840 --> 00:20:00,559 So, these are the index which comprises of something 50 stocks as in case of nifty, 30 230 00:20:00,559 --> 00:20:06,650 stocks in the case of sensex. So, say 30 or 50 shares that comprises that, that is the 231 00:20:06,650 --> 00:20:11,570 index compriser of comprise of they are suppose to repress the broad market. 232 00:20:11,570 --> 00:20:17,330 So, this sensex or nifty for that matter represent the market portfolio, they are not necessary 233 00:20:17,330 --> 00:20:22,590 market portfolio asset. So, what we see how this particular stock is moving, how this 234 00:20:22,590 --> 00:20:29,590 along with the market portfolio. And then, as we discussed it is the risk involved with 235 00:20:31,580 --> 00:20:35,960 the market is called systematic risk, it is this risk relates to the variance of the investment 236 00:20:35,960 --> 00:20:39,860 to the variance of the market. So, how much it is varying with the respect 237 00:20:39,860 --> 00:20:45,929 to the market. So, that is called the systematic risk which will be there, which we cannot 238 00:20:45,929 --> 00:20:49,600 avoid because this is going be that as long as you are investing in the market assets. 239 00:20:49,600 --> 00:20:56,570 So, all the investments, all the shares, all the financial assets are likely to move with 240 00:20:56,570 --> 00:21:01,750 the market and markets movement is the variance is known as variance there. So, what is the 241 00:21:01,750 --> 00:21:06,549 relation, the variance of the investment to the variance of the market is the systematic 242 00:21:06,549 --> 00:21:11,919 risk. So, some of the investments may not move in 243 00:21:11,919 --> 00:21:17,580 the same proportion of the market, it may move in same positive direction, but not necessarily 244 00:21:17,580 --> 00:21:24,580 equally proportionately with the market assets. Then the return that we the systematic risk 245 00:21:25,929 --> 00:21:32,080 that we actually call, we measure in term something called a beta. 246 00:21:32,080 --> 00:21:37,010 Actually when you say beta, it is nothing but the regression coefficient of the returns 247 00:21:37,010 --> 00:21:44,010 on security and returns on market. That means, if you have a series of returns on a security 248 00:21:46,020 --> 00:21:52,630 called i, then you have series of return on security called m on the market portfolio 249 00:21:52,630 --> 00:21:57,490 then we have got something called a date here. So, there are different dates and different 250 00:21:57,490 --> 00:22:03,540 dates the holding period return could be something like this and there will be some returns what 251 00:22:03,540 --> 00:22:09,000 about 10 percent 12 percent 5 percent whatever that may be. Now, when you are on a regression 252 00:22:09,000 --> 00:22:16,000 of this R i, it is called dependent variable on the return of market that is called R m. 253 00:22:16,390 --> 00:22:22,860 So, that whatever slope you get that is called the beta assets a simple regression coefficient. 254 00:22:22,860 --> 00:22:29,860 So, if you can keep in a simple format. So, we have got alpha plus beta R m plus in a 255 00:22:32,900 --> 00:22:36,980 popular term, we have got error term. So, this beta what we are going to get is nothing 256 00:22:36,980 --> 00:22:42,890 but drowning the regression of this return on the security called i th security, which 257 00:22:42,890 --> 00:22:47,760 is also known as a dependent variable. And this return on this security i depends on 258 00:22:47,760 --> 00:22:53,360 the market return that is called the independent variables, so we are saying the security return 259 00:22:53,360 --> 00:22:58,630 depends on the market return. And whatever slope you get here this beta that is called 260 00:22:58,630 --> 00:23:02,490 beta. So, the beta is high obviously, it is suppose to be more risky, beta is less this 261 00:23:02,490 --> 00:23:06,809 suppose to be less risky. So, interpreting beta assets, the beta is 262 00:23:06,809 --> 00:23:13,809 found to be 0.80, it implicates that if there is 1 percent change could be upward or could 263 00:23:13,890 --> 00:23:20,890 be downward in market; that means, the market goes up by 1 percent or market comes down 264 00:23:21,960 --> 00:23:28,960 by 1 percent, then there will be 1 percent change in market then it is going to lead 265 00:23:30,520 --> 00:23:37,520 to 0.8 percent change in the i th stock price. Similarly, the beta is 1.2, see one percent 266 00:23:44,370 --> 00:23:49,799 change in market will lead to 1.2 percent change; that means, when he say 1.2 percent 267 00:23:49,799 --> 00:23:56,740 change, if there is a fall of 1 percent, it will be coming down by 1.2 percent; in a 0.8 268 00:23:56,740 --> 00:24:02,549 percent case, if there is a 1 percent change in market, the rise could be up to this and 269 00:24:02,549 --> 00:24:07,230 the fall could be up to this. So, this difference between these two points 270 00:24:07,230 --> 00:24:14,220 0.8 percent here, 0.8 percent here obviously, is lower than the difference between these 271 00:24:14,220 --> 00:24:21,220 two points. So, the when we say change, change can be upward change can be downward and there 272 00:24:22,740 --> 00:24:27,970 is a variance we can see, we can it go down by 1.2 percent it can go up by 1.2 percent. 273 00:24:27,970 --> 00:24:34,770 So obviously, looking at that higher the beta we say higher the risk. So, the particular 274 00:24:34,770 --> 00:24:40,960 stock which has got higher beta, so we say higher the risk involved in this particular 275 00:24:40,960 --> 00:24:43,600 asset a financial asset for that matter. 276 00:24:43,600 --> 00:24:48,299 So, this is the simpler interpretation of beta which is representing the systematic 277 00:24:48,299 --> 00:24:55,299 risk of the company, the investment which is actually affected by the market risk of 278 00:24:55,990 --> 00:25:01,630 the market risk involved in this investing that particular stock. 279 00:25:01,630 --> 00:25:07,160 Then as we already we have told about that, there is something called fundamental risk 280 00:25:07,160 --> 00:25:10,940 versus systematic risk. Fundament risk comprise of business risk, financial risk, liquidity 281 00:25:10,940 --> 00:25:15,440 risk, exchange rate risk and country risk all those things are there, whereas systematic 282 00:25:15,440 --> 00:25:19,770 risk is something which is the portion of an individual assets total variance attributable 283 00:25:19,770 --> 00:25:26,770 to that variability of the total market. If the risk is x percent, but how much is affected 284 00:25:29,789 --> 00:25:36,789 by the market and how much is affected by the individual stock itself. 285 00:25:37,990 --> 00:25:44,990 So, this is called the systematic risk, there is a very simpler measure also where we have 286 00:25:48,260 --> 00:25:55,260 a concept called coefficient of determination, which is known as the square of correlation 287 00:25:57,840 --> 00:26:04,059 coefficient, you have to known as R, then R square gives you coefficient of determination. 288 00:26:04,059 --> 00:26:11,059 Now, if correlation coefficient is 0.7. So, r square becomes 0.49. So, that says 49 percent 289 00:26:13,929 --> 00:26:20,929 of the risk is affected by the market, when you say correlation we say the correlation 290 00:26:24,530 --> 00:26:31,530 is between the - so, the R is between the - correlation coefficient it is between the 291 00:26:32,720 --> 00:26:39,720 stock return and market return. And we know, the market return is dependent and stock return 292 00:26:42,799 --> 00:26:49,799 is independent. So, the market return is going to affect the stock return. So, 49 percentage 293 00:26:50,250 --> 00:26:57,250 of the risk involved in the stock is affected by the market, which is actually independent 294 00:26:57,960 --> 00:27:01,400 variable. This is another way one can find out the systematic 295 00:27:01,400 --> 00:27:08,400 risk. So, systematic risk portion is 49 percent and on systematic risk is obviously, 51 percent 296 00:27:09,690 --> 00:27:14,510 that is nothing but 100 minus 49 percent. 297 00:27:14,510 --> 00:27:21,220 So, this is the unsystematic risk. So, this 49 percent is market risk, which cannot be 298 00:27:21,220 --> 00:27:28,220 diversified. So, we can diversify due to the extent of 51 percent then, there is this particular 299 00:27:29,070 --> 00:27:36,070 graph shows the risk free rate of return, the nominal risk free of return on the x axis 300 00:27:36,390 --> 00:27:41,049 and the business risk that is your systematic risk, which is measured by beta is on the 301 00:27:41,049 --> 00:27:47,870 y axis. So, sorry the RFR is on the y axis whereas, 302 00:27:47,870 --> 00:27:52,659 the business risk and systematic risk or beta is on the x axis. So, if the business risk 303 00:27:52,659 --> 00:27:59,650 of the particular asset is going up, so that means, if it is moving from 0 to 1 2 3 like 304 00:27:59,650 --> 00:28:06,650 on the x axis. So, depends on that more is the risk, so it will be high, low or average. 305 00:28:08,419 --> 00:28:15,419 So, low risk means the beta is high, as low risk means beta is low that is lesser, average 306 00:28:18,669 --> 00:28:24,559 mean it will more, high risk is little further more and this particular when you plot this 307 00:28:24,559 --> 00:28:28,400 different stocks, different investments on this line, this particular line is called 308 00:28:28,400 --> 00:28:33,750 security market line. It is nothing but the on the x axis we have risk, measured by the 309 00:28:33,750 --> 00:28:39,870 beta of the particular stock and beta is measured as we discussed earlier and on the on the 310 00:28:39,870 --> 00:28:42,570 y axis, we have the rate of return that is expected. 311 00:28:42,570 --> 00:28:48,409 So, we start is something like risk free rate of return that is the graph starts from the 312 00:28:48,409 --> 00:28:54,159 RFR when the business risk is 0, then in that case, you are going to have this much minimum 313 00:28:54,159 --> 00:29:00,679 rate of return and as the risk of the particular asset goes up, if this is so, the return expected 314 00:29:00,679 --> 00:29:04,870 on the investment in different assets go up. So, highest risk is obviously, going to have 315 00:29:04,870 --> 00:29:09,320 highest possible rate of return. 316 00:29:09,320 --> 00:29:14,940 Then what happens in the market, so changes in required rate of return due to movements 317 00:29:14,940 --> 00:29:21,940 along the security market line. So, if there is I feel, the investor feels that the investment 318 00:29:22,750 --> 00:29:26,110 is going to have less risk assets. 319 00:29:26,110 --> 00:29:33,110 So, in that case what will happen? If we had an SML as in the graph that is shown in the 320 00:29:33,720 --> 00:29:39,510 SML like this, then at this point of time, I feel this is the risk involved as for the 321 00:29:39,510 --> 00:29:46,480 investor this is a risk and this is the required that is the return expected by the investor. 322 00:29:46,480 --> 00:29:53,480 So, if this is the risk I am filling, obviously this is the amount of return I expect, that 323 00:29:53,620 --> 00:29:59,289 is nothing but this particular return, but if I feel that the risk of the particular 324 00:29:59,289 --> 00:30:04,409 investment in this particular asset as moved down, let us say from this point to this point, 325 00:30:04,409 --> 00:30:08,320 so in that case, that means, risk is actually moving down from this point to this point 326 00:30:08,320 --> 00:30:14,600 then, my return that I am expecting will be now this much. 327 00:30:14,600 --> 00:30:20,809 So, in the SML as I move upwards, my return is going to be higher as I move downwards 328 00:30:20,809 --> 00:30:25,080 my return is going to less; moving upwards means I am going a high risk. So, it is not 329 00:30:25,080 --> 00:30:30,030 necessary that for every time to come the risk involved in a particular asset is going 330 00:30:30,030 --> 00:30:35,059 to be constant, rather it can go down or it can also go up, if goes up to this particular 331 00:30:35,059 --> 00:30:42,059 point, then my return will be little that I have expect little bit in R2 is little more, 332 00:30:42,220 --> 00:30:45,559 because the risk involved in a particular asset actually has to less gone up. 333 00:30:45,559 --> 00:30:52,390 So, that is the change in the position of a particular stocks return in a particular 334 00:30:52,390 --> 00:30:58,240 SML, so this is a movement from high risk to little lower and further little lower to 335 00:30:58,240 --> 00:31:02,090 further lower risk involved in that. 336 00:31:02,090 --> 00:31:09,090 Next, in fact, we estimate like this, where you say risk premium is nothing but expected 337 00:31:09,720 --> 00:31:15,640 rate of return minus the nominal rate risk free rate of return. So, this is the difference 338 00:31:15,640 --> 00:31:22,640 assets risk premium and so change in this slope can also be… So, slope means I have 339 00:31:23,470 --> 00:31:30,470 a presently the SML is like this. So, this is my slope, this is relation between 340 00:31:31,650 --> 00:31:38,350 this and this means gives the slope, but that means, for every additional unit of risk, 341 00:31:38,350 --> 00:31:44,720 I expect a particular amount of return, but the slope itself may go up. So, in that case 342 00:31:44,720 --> 00:31:50,010 the line will change. So, the slope is going to be higher that means, at this point of 343 00:31:50,010 --> 00:31:57,010 time, the investor is expecting a reward for any unit of risk invest little more reward 344 00:31:57,039 --> 00:31:59,059 than what he was expecting earlier. 345 00:31:59,059 --> 00:32:03,029 So, the slope of the line is changing, now possibly in depending on the market condition 346 00:32:03,029 --> 00:32:09,350 I may expect little much more risk, this will more return than this particular graph where 347 00:32:09,350 --> 00:32:16,350 my slope is actually higher. So in that case, I am expecting more return on the investment 348 00:32:17,179 --> 00:32:22,539 depending on the risk involved. Earlier, if I was expecting let say 1 percent 349 00:32:22,539 --> 00:32:27,470 extra per unit of risk involved now, I may expect the 1.2, so the beta might have gone 350 00:32:27,470 --> 00:32:34,470 up from one stage to another stage. So, in that case it will be going to be more as such. 351 00:32:35,710 --> 00:32:42,409 So, the market risk premium for the portfolio can also be found out. So, where we say that, 352 00:32:42,409 --> 00:32:49,409 the market portfolio risk return as such is nothing but expected return and minus the 353 00:32:49,590 --> 00:32:50,840 nominal risk free rate of return. 354 00:32:50,840 --> 00:32:57,840 That means if my expected rate of return is 18 percent that is on the portfolio, then 355 00:32:59,340 --> 00:33:06,340 if the nominal risk free rate of return is let say 8 percent; that means, the risk premium 356 00:33:07,049 --> 00:33:10,730 on the market, I am taking is how much is called 10 percent. 357 00:33:10,730 --> 00:33:15,679 So, this is nothing different than any individual asset also, instead of talking on individual 358 00:33:15,679 --> 00:33:19,580 asset, you are talking about a combination of the financial assets called the portfolio. 359 00:33:19,580 --> 00:33:26,320 So, the risk premium measurement is the almost same as what do you do in an individual asset 360 00:33:26,320 --> 00:33:29,370 as well as in the portfolio assets. 361 00:33:29,370 --> 00:33:36,370 So, this is one place where we have got this SML changing from one place to another that 362 00:33:37,059 --> 00:33:43,480 has you discuss in the graph. So, there is what is happening here? Whatever risk return 363 00:33:43,480 --> 00:33:50,480 they were expecting for risk involved as actually that per unit per unit risk, the return is 364 00:33:50,840 --> 00:33:55,539 expected is actually going up. That is why the SML has moved from one stage to another 365 00:33:55,539 --> 00:33:58,909 stage, in some other case also the SML can come down. 366 00:33:58,909 --> 00:34:05,909 So, where you have a SML like this, since I am expecting that my expectation is something 367 00:34:06,210 --> 00:34:12,270 that my return I expect from the risk involve has come down, so the SML in this case what 368 00:34:12,270 --> 00:34:17,990 will happen if I am my I my asset return comes at this particular point of time and if I 369 00:34:17,990 --> 00:34:24,510 am expecting that reward per risk is going to come down, my expectation is like that 370 00:34:24,510 --> 00:34:27,230 then the slope of the particular graph will be lower. 371 00:34:27,230 --> 00:34:33,869 Now, I will be expecting this much return, but the same type of asset, but I am going 372 00:34:33,869 --> 00:34:39,399 to expect rates return and this is called the risk free rate of return. So, I will be 373 00:34:39,399 --> 00:34:45,399 expecting this much extra, earlier I was expecting this much extra. Though the asset class has 374 00:34:45,399 --> 00:34:52,200 not changed it has remain this same, but since the return I expects the for the risk involved 375 00:34:52,200 --> 00:34:58,080 is lower, that is why my return expected from this asset has now come down from here, may 376 00:34:58,080 --> 00:35:01,359 be it was 12 percent could have become now 10 percent. 377 00:35:01,359 --> 00:35:08,359 So, this is the way this is an original security market line and this is my new security market 378 00:35:10,230 --> 00:35:17,230 line. Here we talked about original SML, and then we had new SML 1 and new SML 2, where 379 00:35:22,670 --> 00:35:27,760 the return expected per unit of risk involved as actually gone up from to one stage to another 380 00:35:27,760 --> 00:35:31,170 stage to another stage. 381 00:35:31,170 --> 00:35:38,170 Then overall in the market itself the expect return from the in the market may go up because, 382 00:35:39,280 --> 00:35:46,280 there is a change in the risk free rate of return. So, earlier I was expecting an inflation 383 00:35:48,609 --> 00:35:55,609 of 5 percent. So, in that I keep factoring that, my risk 384 00:35:56,540 --> 00:36:03,540 free rate of return was let say 8 percent for whatever is in, the inflation has either 385 00:36:03,849 --> 00:36:08,530 gone up or come down let say inflation has become now 7 percent. So, quite naturally 386 00:36:08,530 --> 00:36:15,530 my RFR will now move up from 8 percent to at least 10 percent, if you have to have a 387 00:36:16,580 --> 00:36:20,800 simple addition of 2 percent difference between this inflation earlier and inflation now, 388 00:36:20,800 --> 00:36:24,070 then 2 percent plus 8 percent becomes now 10 percent. 389 00:36:24,070 --> 00:36:31,070 In that case the graph which you had started, the SML which are started, the old SML which 390 00:36:31,490 --> 00:36:38,490 are started at this point since RFR it is changing it becoming this one then graph will 391 00:36:40,820 --> 00:36:45,390 just move upward without any change in the slope of the graph. So, this becomes a new 392 00:36:45,390 --> 00:36:51,190 SML. Now, if I had a class of asset like A, I had 393 00:36:51,190 --> 00:36:58,190 A class of asset like B and I had class of asset called C, if I was expecting here I 394 00:36:59,560 --> 00:37:05,280 was expecting let say 9 percent, here I was expecting let say 11 percent, here I was expecting 395 00:37:05,280 --> 00:37:11,470 actually 13 percent these are the percentage here, then since this RFR itself has gone 396 00:37:11,470 --> 00:37:18,470 up from 8 percent to 10 percent so obviously, this 9 will now become 11 percent and this 397 00:37:20,920 --> 00:37:24,080 11 will become now 13 percent and 13 will become now 15. 398 00:37:24,080 --> 00:37:30,589 So, there is an upward parallel shift in the SML from old to the new. Similarly, if the 399 00:37:30,589 --> 00:37:36,200 I expect the risk involved in the overall market is going to be now lower, then in that 400 00:37:36,200 --> 00:37:42,220 case my RFR itself may come down from 8 percent to let say 6 percent because of change in 401 00:37:42,220 --> 00:37:46,910 inflation, lower inflation whatever that may be, in that case, I will have a new SML which 402 00:37:46,910 --> 00:37:51,890 will start from the RFR of 6 percent and which will be parallel to the olden. 403 00:37:51,890 --> 00:37:56,750 So, what you are saying? Here we are assuming that, the per unit risk whatever return I 404 00:37:56,750 --> 00:38:02,580 am going to get is not going to change, rather the base of risk free return as change. So, 405 00:38:02,580 --> 00:38:08,450 the overall SML itself has either gone up, moved up or it has gone down depending on 406 00:38:08,450 --> 00:38:11,359 the RFR condition. 407 00:38:11,359 --> 00:38:18,260 Now, we go to the next part of this particular class, where you talk about how we measure 408 00:38:18,260 --> 00:38:21,869 the portfolio return and portfolio risk. Earlier class we have already discussed the portfolio 409 00:38:21,869 --> 00:38:28,040 return, but we can also repeat that now. So, the return on a portfolio depends upon the 410 00:38:28,040 --> 00:38:34,310 weights involved in the assets, that we have and the individual return. So, if you have 411 00:38:34,310 --> 00:38:40,710 about 2 assets called asset called A and asset called B and if we are going have 14 percent 412 00:38:40,710 --> 00:38:44,849 return from asset A and 16 percent return on asset B. 413 00:38:44,849 --> 00:38:51,849 And if your weight is involved is let say 0.50, 0.50 on both the assets, asset called 414 00:38:52,420 --> 00:38:59,260 A asset called B, that is the weight of investment and if we are expecting return on asset called 415 00:38:59,260 --> 00:39:05,599 A as 14 percent and asset called B as let say 16 percent. So, the return on the portfolio 416 00:39:05,599 --> 00:39:11,849 is the return on the asset called i th asset called A or B. So, returns on portfolio have 417 00:39:11,849 --> 00:39:18,849 been now 0.50 into 14 percent plus 0.50 into 16 percent. So, that gives us 7 percent plus 418 00:39:19,710 --> 00:39:25,780 8 percent that is gives you 15 percent return on the portfolio say between 14 and 16 percent 419 00:39:25,780 --> 00:39:29,599 now. So, if the weights change from 50 50 to 40 420 00:39:29,599 --> 00:39:36,190 60, so accordingly portfolio return is also going to change. So, this is only a two asset 421 00:39:36,190 --> 00:39:39,960 scenario, you can have n number of assets and obviously, for n number of assets we need 422 00:39:39,960 --> 00:39:45,160 to have the weights of the different assets, as well as the return expected from the different 423 00:39:45,160 --> 00:39:46,420 assets access. 424 00:39:46,420 --> 00:39:53,420 So, we can look at another example where we have got 3 or 4 assets, where we got 20 percent 425 00:39:55,060 --> 00:40:02,060 asset 20 percent on investment in A, 30 percent of investment in the asset B and 40 in C and 426 00:40:02,690 --> 00:40:08,320 10 percent in the asset called D. And the expected return from the each asset is like 427 00:40:08,320 --> 00:40:15,210 this that means, 18 percent, 16 percent, 20 and 24 applying the same formula you multiply 428 00:40:15,210 --> 00:40:20,839 0.2 there are 20 percent into 0.18. Accordingly like that for assertive, we multiply 429 00:40:20,839 --> 00:40:26,140 0.10 and 0.24. So, overall that you will get is 15.8 percent; that means, in an extreme 430 00:40:26,140 --> 00:40:33,140 case, if I had put money 100 percent the asset called C and then in that case, I would have 431 00:40:33,589 --> 00:40:38,000 got 20 percent had I put 100 percent asset called B, I would have got 16 percent that 432 00:40:38,000 --> 00:40:41,310 is the lowest return and the C is giving highest return. 433 00:40:41,310 --> 00:40:47,609 But instead of that, because I may feel that asset called C may actually go up or come 434 00:40:47,609 --> 00:40:53,910 down it may more risk involved. So, to diversify to have a many more return assets sum is assured 435 00:40:53,910 --> 00:40:58,960 rate of return, they instead of putting money all money into one asset called C, I now put 436 00:40:58,960 --> 00:41:03,240 money into four different assets and that expect return is combination of that is called 437 00:41:03,240 --> 00:41:07,480 15.8 percent is the return expected from the portfolio. 438 00:41:07,480 --> 00:41:13,430 It is the very simple principle that we say, do not put all x in one basket rather you 439 00:41:13,430 --> 00:41:18,050 keep different x in different basket. So, the one basket is lost, at least some of the 440 00:41:18,050 --> 00:41:23,099 x are still left which you can be consumed by the consumer, you otherwise all the if 441 00:41:23,099 --> 00:41:28,420 you are putting in one particular asset all your money 100 percent money is I may go up 442 00:41:28,420 --> 00:41:33,079 like anything if the market is moving up or it may also, can also come down if the market 443 00:41:33,079 --> 00:41:33,490 is down. 444 00:41:33,490 --> 00:41:40,490 So, in that case, we rather diversified portfolio by investing in different assets. Next thing 445 00:41:41,970 --> 00:41:47,570 that we have is called the portfolio risk. Portfolio risks nothing but the variance involved 446 00:41:47,570 --> 00:41:54,570 in the portfolio. So, if one is able to find out the variance in the individual asset then 447 00:41:54,650 --> 00:41:56,910 one can also find out the variance in the portfolio. 448 00:41:56,910 --> 00:42:03,910 Now, if I have got in the earlier case, when you have got return on different condition 449 00:42:05,380 --> 00:42:12,380 1, condition 2, condition 3 and condition 4, it could be the best economy condition 450 00:42:16,079 --> 00:42:21,550 this could be very good condition, this could be an average conditions, this could be poor 451 00:42:21,550 --> 00:42:23,920 condition. So, for a particular stock, if you are expecting 452 00:42:23,920 --> 00:42:30,780 let say 12 percent in the best condition, then 10 percent in the little worst condition, 453 00:42:30,780 --> 00:42:36,960 then 8 percent and then 6 percent, these are the condition, for that we also should have 454 00:42:36,960 --> 00:42:42,849 the probability associated with this particular event condition 1 to condition 4. So, you 455 00:42:42,849 --> 00:42:49,849 have let say 20.25, 0.30, 0.40 and the rest is 0.05. So, what we do, we multiply like 456 00:42:56,510 --> 00:43:03,510 this, so 0.25 into 12, 0.30 into - so, this total is actually 1.00 - 0.30 into 10 percent 457 00:43:05,760 --> 00:43:12,760 0.40 into 8 percent and 0.05 into 6 percent. So, what we get here is that 12.12 into 0. 458 00:43:16,950 --> 00:43:23,950 25 that give 0.03, this also gives 0.03, then we got 0.032 and then we have got 0.030. So, 459 00:43:28,609 --> 00:43:35,609 say total of this gives you us to and so, 0.122 to that is 12.2 percent is the returns 460 00:43:40,099 --> 00:43:45,440 from the asset expect return depending on four different conditions. So, like that we 461 00:43:45,440 --> 00:43:48,540 do here, we can also do the same thing for a portfolio. 462 00:43:48,540 --> 00:43:54,540 So, what you do here is that this 12 percent or 10 percent whatever that you have expected 463 00:43:54,540 --> 00:44:00,079 from the return in the stock, we have to now measure that from the portfolio it is and 464 00:44:00,079 --> 00:44:03,760 this particular 12 percent in the return on a portfolio, it will depend upon obviously 465 00:44:03,760 --> 00:44:10,760 as you discuss earlier, it will be w1 into r1 plus w2 into r2 like that we have got w 466 00:44:11,260 --> 00:44:18,200 n into r n. So, whatever you get, we now get r p under condition 1, similarly condition 467 00:44:18,200 --> 00:44:23,420 2, condition 3, condition 4 whatever return you get and then multiply with respect probability 468 00:44:23,420 --> 00:44:28,990 then you get return on the portfolio. So, in the risk calculation what you will 469 00:44:28,990 --> 00:44:35,359 do? We take the difference between the return that is 12 percent and the average return 470 00:44:35,359 --> 00:44:42,359 and square it and then we multiply with the respective. So, what we do here? We say 0.12 471 00:44:43,690 --> 00:44:50,690 minus 0.122 in the first case and we square it and multiply the respective rolled in the 472 00:44:51,000 --> 00:44:56,950 case 0.25, like that you do and when you add that summation that gives actually variance 473 00:44:56,950 --> 00:45:01,839 or sigma square and you take the square of the variance that gives us the standard deviance, 474 00:45:01,839 --> 00:45:08,109 that is called the variance square root. So, same principle is applied as far as the 475 00:45:08,109 --> 00:45:13,630 return as per the risk of the portfolio is concerned. So, what you do here assuming that 476 00:45:13,630 --> 00:45:17,920 this is the portfolio return, average return and these are the different returns and different 477 00:45:17,920 --> 00:45:22,619 circumference in the portfolio. So, in that case, 12.2 percent is the average return and 478 00:45:22,619 --> 00:45:28,190 I we can found out the variance in the same measure, that same way that we did in the 479 00:45:28,190 --> 00:45:32,240 previous session as far as a risk in this individual asset is concern. 480 00:45:32,240 --> 00:45:39,240 This is one way and another way that we have is that, we find out the movement in the assets, 481 00:45:43,030 --> 00:45:47,410 how they move with each other and how they move along with the market and based on that 482 00:45:47,410 --> 00:45:52,050 also one can find out the portfolio instead of doing a weighted return of the portfolio 483 00:45:52,050 --> 00:45:55,369 and finding on this way, we can also find out in another which we will be discuss in 484 00:45:55,369 --> 00:45:56,359 subsequent slide. 485 00:45:56,359 --> 00:45:59,780 So, risk of the portfolio actually depends on the risk of the individual asset of the 486 00:45:59,780 --> 00:46:05,730 portfolio and the covariance of returns of assets in the portfolio; that means, if the 487 00:46:05,730 --> 00:46:10,890 there are assets in a portfolio like A, B, C and D. 488 00:46:10,890 --> 00:46:17,800 So, risk of the portfolio which comprises of this four assets, will depend upon the 489 00:46:17,800 --> 00:46:23,010 risk of individual asset like A, B, C and D and how they move with each of them, how 490 00:46:23,010 --> 00:46:29,210 A moves along with B, how B along with move A, how A moves along with C and how C moves 491 00:46:29,210 --> 00:46:34,260 along with A and how A moves along with the D and D moves along with the A. 492 00:46:34,260 --> 00:46:40,020 Similarly, what the how is the D and C are related, then how C and B are related and 493 00:46:40,020 --> 00:46:45,980 how D and B are related and how C and A related; that means, as many pairs that can be possible 494 00:46:45,980 --> 00:46:50,130 about the relationship. So, this movement is also going to affect the risk of the portfolio. 495 00:46:50,130 --> 00:46:55,440 So, it is not only the risk involved in A, B, C or D rather, how they move with each 496 00:46:55,440 --> 00:47:00,030 other that is also going to affect the reason. And they moving with each other are called 497 00:47:00,030 --> 00:47:06,020 the covariance. So, covariance could be there, there could be covariance between A and B, 498 00:47:06,020 --> 00:47:13,020 covariance between B and C, C and A, B and D, C and D like that as many pairs as possible 499 00:47:15,990 --> 00:47:21,200 there is covariance. So, this all these covariance as well as variance of individual stock like 500 00:47:21,200 --> 00:47:26,000 standard, it was a standard set B standard deviation C and standard deviation D all these 501 00:47:26,000 --> 00:47:29,040 things are going to affect the variance of particular portfolio. 502 00:47:29,040 --> 00:47:34,790 So, one should not take that variance of a portfolio is simple, the average of the variance 503 00:47:34,790 --> 00:47:39,339 of individual assets in that portfolio. If individual asset the portfolio affect the 504 00:47:39,339 --> 00:47:43,329 portfolio of a variance as well as the how the individual security are varying with each 505 00:47:43,329 --> 00:47:47,079 other, that is also going to affect. That means if one asset is going upward another 506 00:47:47,079 --> 00:47:51,200 asset is going to downward, so that means, risk involved in one asset is compensate by 507 00:47:51,200 --> 00:47:58,200 the risk in another asset as such. So, any gain in asset A is now neutralized by a loss 508 00:47:58,720 --> 00:48:04,470 in asset B or another way you can say a loss in asset B is now neutralized by A gain in 509 00:48:04,470 --> 00:48:05,069 asset A. 510 00:48:05,069 --> 00:48:10,190 So, that case the risk is going to be reduced. So, risk of the portfolio is expect to be 511 00:48:10,190 --> 00:48:14,790 reduce with inclusion of more assets in the portfolio, but there is a cell, it is not 512 00:48:14,790 --> 00:48:18,470 necessary that you have to can increase the portfolio size in terms of number of assets 513 00:48:18,470 --> 00:48:24,069 to as many numbers of assets. There could be a limit optimal limit up to there is 30 514 00:48:24,069 --> 00:48:28,980 40 stocks if you can have, then the portfolio can be taken as well diversified portfolio. 515 00:48:28,980 --> 00:48:33,119 In a two asset portfolio, return and one asset is negatively correlated of the portfolio 516 00:48:33,119 --> 00:48:37,680 risk is going to be lower, when the returns of assets are positively correlated; that 517 00:48:37,680 --> 00:48:44,680 means, if we have to club make a graph this is the price of an asset. 518 00:48:55,810 --> 00:49:02,810 Let me go back to this graph once again, this is the time line of an asset and this is the 519 00:49:10,530 --> 00:49:15,970 price of the asset, the time line of the investment. So, if even asset called A which is moving 520 00:49:15,970 --> 00:49:22,970 like this and you also have an asset B, which is also moving like this, almost parallel 521 00:49:29,369 --> 00:49:36,369 to asset B, then there will not be any direction, the diversion diversification if we are having 522 00:49:38,400 --> 00:49:44,109 100 percent A and now you are having 50 percent and 50 percent B in asset composition, in 523 00:49:44,109 --> 00:49:48,760 that case the risk is not going to this because the B is moving in tandem with my a asset. 524 00:49:48,760 --> 00:49:52,569 But, that means, there is a rise here, there is also rise, there is a fall there is also 525 00:49:52,569 --> 00:49:56,869 fall here. So, they are not neutralizing each other; that means, obviously one can find 526 00:49:56,869 --> 00:50:01,180 out this is a positive correlation and very high possibly correlation could be one here. 527 00:50:01,180 --> 00:50:08,060 But, if you have a scenario asset A is moving like this whereas, asset B is moving like 528 00:50:08,060 --> 00:50:15,060 this, in that case if there is an upward movement in asset A, there is a downward movement asset 529 00:50:18,300 --> 00:50:25,300 B. So, they neutralizes each other some over return may fall in line between these two 530 00:50:25,390 --> 00:50:29,609 and obviously in this case, the fluctuation is not be seen and there is no fluctuation 531 00:50:29,609 --> 00:50:33,359 invest in the portfolio of A and B; that means, the report free risk is actually reduce. 532 00:50:33,359 --> 00:50:39,569 So, if you can have two assets which are perfectly negatively correlated, then the risk can be 533 00:50:39,569 --> 00:50:45,960 reduced to the maximum extent. So, positive correlation between stocks will lead to less 534 00:50:45,960 --> 00:50:52,960 risk, less diverse in the risk assets than high positive correlation between stock returns. 535 00:50:53,160 --> 00:51:00,160 So, as you suggested earlier, there is an alternate measure of risk here, what will 536 00:51:02,150 --> 00:51:09,150 happens here? As you discuss again, the portfolio risk depends upon the individual risk that 537 00:51:10,410 --> 00:51:14,859 is the standard deviation i th asset, weight involved in the particular asset as well as 538 00:51:14,859 --> 00:51:20,050 the covariance between the i th asset and j th asset, i can go from 1 to n, j can also 539 00:51:20,050 --> 00:51:24,930 go from one to n. And so, portfolio is standard deviation of 540 00:51:24,930 --> 00:51:29,710 the portfolio, where the weights are assigned as far the combination of asset and the variance 541 00:51:29,710 --> 00:51:33,670 of returns is given on the asset i then, we have the covariance; that means, we need to 542 00:51:33,670 --> 00:51:38,200 have the covariance between two asset return, we also should have the variance of the one 543 00:51:38,200 --> 00:51:40,970 asset return in the individual asset in the portfolio. 544 00:51:40,970 --> 00:51:47,970 Then if you look at this particular example, we have the asset R, asset called A and B 545 00:51:51,220 --> 00:51:57,170 where you have got 10 percent return expect return and 20 percent expect return is there 546 00:51:57,170 --> 00:52:03,420 in asset B. And weights attached to these two stocks are 0.50 and 0.50, the 50 percent 547 00:52:03,420 --> 00:52:10,420 weight is there and the variance is 0.0049 and 0.0100 then, we go to find out the standard 548 00:52:12,260 --> 00:52:13,730 0.07 0.10. 549 00:52:13,730 --> 00:52:20,109 The standard deviation portfolio is nothing but what you do here. The weight square the 550 00:52:20,109 --> 00:52:27,109 0.5 and 0.5 then, if you go back to the graph. So, the equation we have got W 1 square and 551 00:52:27,859 --> 00:52:31,359 standard deviation 1 square, then we will have W 2 square and standard deviation 2 square, 552 00:52:31,359 --> 00:52:32,849 so like that it has been done. 553 00:52:32,849 --> 00:52:38,560 So, this one gives us the W 1 square, this one gives us the standard deviation one square, 554 00:52:38,560 --> 00:52:44,690 this one gives the W 2 square, in this case both the assets have got 0.5 and 0.5 weight 555 00:52:44,690 --> 00:52:51,690 age. So, this got 0.20 this is a 0.20. Then this is the relations between asset A and 556 00:52:52,290 --> 00:52:58,700 asset B, this relation between asset B and asset A. So, in a 2 portfolio context, actually 557 00:52:58,700 --> 00:53:02,740 these one the third component of this equation and the fourth component that was is nothing 558 00:53:02,740 --> 00:53:03,890 but one and same. 559 00:53:03,890 --> 00:53:10,890 So, what happens in equation format, the portfolio return in a 2 port towards asset portfolio, 560 00:53:11,260 --> 00:53:18,260 this is a variance; then we have got W 1 square standard deviation 1 square plus W 2 square 561 00:53:18,470 --> 00:53:25,470 into standard deviation 2 square. Then we have got W 1 standard deviation 1 and then 562 00:53:28,940 --> 00:53:35,940 covariance 1 2, then you have got W 2 standard deviation 2 then, we have got covariance 2 563 00:53:43,140 --> 00:53:50,140 1. So, essentially this becomes one and same. W 1 and W 2 and W 2 into W 1 and instead of 564 00:54:05,050 --> 00:54:10,339 standard deviation or a standard deviation two assets. So, covariance 2 and 1 and covariance 565 00:54:10,339 --> 00:54:16,980 1 and 2 is same as covariance 2 and 1. So, if you have to simplify this equation, it 566 00:54:16,980 --> 00:54:22,400 becomes W 1 square standard deviation 1 square plus W 2 square standard deviation 2 square 567 00:54:22,400 --> 00:54:29,400 and see these two component becomes one and same, it becomes now 2, W 1 W 2 and covariance 568 00:54:29,990 --> 00:54:36,569 1 and 2. And this covariance between two stocks two 569 00:54:36,569 --> 00:54:41,810 stocks return depends upon the correlation between stock 1 and stock 2 return and the 570 00:54:41,810 --> 00:54:46,270 standard deviation of 1 and standard deviation of 2. So, if somebody has the correlation 571 00:54:46,270 --> 00:54:51,500 between this stock return and the individual standard deviation of the returns of stock 572 00:54:51,500 --> 00:54:57,319 1 and stock 2, then no need to go for a calculation, one can replace these with the covariance 573 00:54:57,319 --> 00:54:58,309 of the stock assets. 574 00:54:58,309 --> 00:55:04,960 So, if you go to the equation what we have done is, we have taken the 0.6 the correlation 575 00:55:04,960 --> 00:55:11,890 coefficient and 0.6 into 0.07 0.10 gives the covariance of the between 1 and 2 or as well 576 00:55:11,890 --> 00:55:13,869 as 2 and 1. 577 00:55:13,869 --> 00:55:20,700 So, if you go further, you will get a simpler excel sheet, in this case we have to take 578 00:55:20,700 --> 00:55:25,230 the portfolio risk you are calculating in a 2 security portfolio. So, there is A and 579 00:55:25,230 --> 00:55:31,890 B and weights are 0.5 and 0.5, and standard deviation return is 0.15 and 0.12 and correlation 580 00:55:31,890 --> 00:55:35,559 is 0.80. So, portfolio of variance by applying the 581 00:55:35,559 --> 00:55:42,559 formula is now 0.0164 and standard deviation 0.1282, if somebody if one there is a 0.80 582 00:55:43,880 --> 00:55:49,430 means high positive correlation. As you discussed earlier, low positive correlation will leads 583 00:55:49,430 --> 00:55:56,430 the risk and if because negative becomes much less risky assets, so if I one change it from 584 00:55:58,349 --> 00:56:03,630 0.80 let say 0.50 on the portfolio standard deviation which changes from 0.1282 now become 585 00:56:03,630 --> 00:56:08,510 0.1172. If somebody makes it minus 0.5, now 0 .117 586 00:56:08,510 --> 00:56:15,510 has become 0.0687. So, this is the thing when what happens is that, with less positive correlation 587 00:56:15,670 --> 00:56:19,480 or risk of the portfolio comes down, when becomes negative, the risk of the portfolio 588 00:56:19,480 --> 00:56:22,990 becomes much lesser. In a three security portfolio what you will 589 00:56:22,990 --> 00:56:27,730 need? We need the weights involved in three securities, we need the weights the standard 590 00:56:27,730 --> 00:56:32,250 deviation also of three securities, but we need the correlation between A and B, B and 591 00:56:32,250 --> 00:56:37,339 C, and C and A all the compression of assets have to there. Then accordingly the variance 592 00:56:37,339 --> 00:56:43,190 can also be found out with this input and we get in the three portfolio three asset 593 00:56:43,190 --> 00:56:49,490 portfolio, where 35 percent A and 40 percent B and 25 percent C is there total is 100 percent. 594 00:56:49,490 --> 00:56:54,960 The portfolio standard deviation is not 0.1369, if somebody changes this makes from any another 595 00:56:54,960 --> 00:56:59,770 makes to it another makes, then also the standard deviation is going to change. So, if in this 596 00:56:59,770 --> 00:57:06,540 case, we make this point in the two asset portfolio make 0.6, now you make it 0.40, 597 00:57:06,540 --> 00:57:11,260 then the standard deviation has change from something we can add it become 0.0780. 598 00:57:11,260 --> 00:57:17,500 Now, similarly that means, weights of the assets of portfolio and the individual assets 599 00:57:17,500 --> 00:57:23,380 risk and the relation between two different assets return that changes, that makes the 600 00:57:23,380 --> 00:57:30,380 portfolio risk asset. So, this is way we covered how to calculate the risk of the portfolio 601 00:57:32,490 --> 00:57:33,530 involved. Thank you.