Question

2. (10 marks) Fill in the missing information assuming a correlation of -0.1. Standard Estimated Return 13% 31% Portfolio Weights Stock A Stock B 100% 80% 60% 40% 20% 0% T 16% 42% Discuss the diversification of this 2-stock portfolio and illustrate in a graph the risk-return trade-off.

Answer 1

- Expected Return = WARA + CUBRE where WA = weight of stock a 1. W8= weight of stock B RA= Retum on stock A Roc Return on stock B Standard deviahon J WAGA+ was a + 22 PAB X WAX CUB XOA XaB where was weight of Stock A WB² weight of stock B OA = std. deviation of stock a ab: Std. deviation of stock B PAB a correlation coefficient between stock A & Stock B Scanned with SCS CamScanner

ng a 101_ Stock A=100% or 1 then stock B = 0% Estimated Return = WARA + WB RB 0.13 = 1(x) + ORB So, 0.13 z lx - x = 0.13 or 13% Stock A = 13% 03 canned Soth Return on CamScanner

a) sid. deviation z JW2 a ² + wg²a8² + 2X PARX CUBX WA xax OB 0:31 - Juan?) +(0)%a8?) + 2x60,7) (011) (AA) (08) 0.31 z ar toto oop (0.31)²= a or 31% of stock A z 03 aA z 0.31 _ So, Standard deviatim Scanned with CamScanner 31% 04

b) Stock A = 0% then stock B 2 05 100% or 1 06 So, Estimated Return = WA RA+ We Rb Notes 0.16 = ORA + 1 (RB) 0.162 1 RB RB = 0.16 or 16% → Return on Stock B Iccl Scanned with CamScanner

b) Srd. deviation = vwzo +w ag²+ 2 x PARX WAX WA xoxo 06 0:42 = √(0)²a²+(122 B + 2(-0.1)(1)(0) (0A) COB Notes 0.42 = vo +98 +0 (0.42)² = 0 AB= ca Scanner ve Standard CamScanner 0.42 or 42% deviation of stock B = 42%

I so, RAF 13% RB = 16% AA 2 31° a82420% (Return on stock A) (Return on stock B) Csta. deviation of shoell A) (stel. deviation of Shock B) Now, Stock A = 80% or 0.8 then stock B = 0.2 I 2 Estimated Return WARA F WB RB z 108 10:13) + (0-2)(0.167 La 0.136 og T 13.6% I Std. deviations wit až was ag + 2 (pac)(c)(W) (90) (03) 05 206] _ =0.0)2(0.31)2 +00:2)2(0:42)2+2 (0:1)(0.81(0:2)(0.31) (0.42) colo.2009 st = 10.0644 Votes - 0005231000 $20389%<0.2537 on 25.37% CS Scanned with camScanner

09 Now, Stock A = 60% then stock B = or 0.6 0.4 - Estimated Return a WARAT WB RB z (0.6) (0.13) + (0.4)(0.16) 2 00142 114,20% Sid. deviation ? / Wa a à t we ca + 2Cle) (Wa)(WB) lan) (ao) 27 (0.6)2(0:31)20.42 (0.42)+ 21-0oll (0.6)10.4)(0431) 10.42) T0.0566 20.2378 or 23.78% Notes Scanned with CamScanner

I now stock A z 40% , then stock B = 60% ono 2. Estimated Returna WARAT WB RB .. 210.420113) + (0.6).CO. 16) _ 2 0.148 3 _ bil 14.8% 05 Std. dewlatina Vwzakrway + 2048) (WA)(WB) Cax)(08) L 061 z 10.492 (0.3122 + (016)2(0422 + 26-0:1)0.4)(0-6)(0-31) C0.42) Notes < 0.0726 2 0.2695 or 1 26.95% Scanned with CamScanner

09 Mbw, Stock A = 20% of 0.2 then Stock Bz00% or 0.8 Estimated Retom a WARA & WB RR 2 (0.2)(0.13) + (0.0) (0.16) z 0.154 or [ 15.4%) std.deviation / WA² at wa + 2(PAB) (UA)(WB) (AA) (98) 041 10.2)2(0:3172+0.01210.42)2 + 21-0.160.210.89(0-31). 10.421 z ✓ 0.1126 06) of 133.55%! ca Scanned with 0 : 3355 CamScanner

final Table Portfolio weight Stock A I Stock B Estimated Return standard deviahon 100°C 13% . 31% 25,37% @09% 20% 13.69% 60% 40% 14.2% 23.789% 40% 6096 14.8% 26.95% 80°% 20% 15:49% 33.55% 100% 16% 42°%. Scanned with CamScanner

So, it can be seen that the with different level of diversifications, the resultant estimated return and standard deviation or risk of the portifolio varies. It we take 100% of stock A, then the risk is higher and return is less if we compare it with the portfolios with proportion of stock A is 20%, 40% and 60% and if we compare it with the portfolios where proportion of stock A is 80% and 100%, then the risk is also higher and return is also higher. The highest level of risk and highest level of return is where the proportion of stock B is 100%. And if we want to have the proportion of both the stocks then the highest return is in the case where proportion of stock A is 20% and stock B is 80%.

GRAPH OF RISK-RETURN TRADE-OFF

Book1 - Excel Chart Tools nitin arora - O X SeBio File Home Insert Page Layout Formulas Data Review View Help Design Format ? Tell me what you want to do Share Chart 3 x fic SERIES(Sheet1!$E$4,Sheet1!$C$5:$C$11,Sheet1!$E$5:$E$11,2) - A B C D E F G H I J K L M N O P Q R S | Risk-Return Trade Off 0.45 0.4 Portfolio Weight Stock A Stock B 100% 0% 80% 20% 60% 40% 40% 60% 20% 80% 0% 100% 0.35 Estimated Return 15% 13.60% 14.20% 14.30% 15.40% 18% Standard Deviation 31% 25.37% 23.78% 26.95% 33.955% 42% 0.3 20% O 0.25 O O 0.2 0.15 0.1 13% 13.60% 14.20% 14.80% 15.40% 16% Sheet1 Ready @ J - + O Type here to search + 100% 01:57 ENG 23-03-2020 6 O A 9 e ? ^ . - 1» a

The above graph is of Risk-return Trade off where returns are taken on X-axis and risk or standard deviation is taken on Y-axis. So, as the proportion of Stock A decreases and stock B increases the estimated returns first decreases and then increases.