question archive Assume that we have only two following risk assets(stock 1 and 2) in the market
Assume that we have only two following risk assets(stock 1 and 2) in the market
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Assume that we have only two following risk assets(stock 1 and 2) in the market. E(r) or) stock 1 20% 20% stock 2 10% 20% The correlation coefficient between stock 1 and 2 is zero(0) and the risk-free asset is 5%. In the equilibrium (i.e., when the prices are properly set or arbitrage transactions are not possible), the market capitalization of stock 1 and 2 are $3 million and $1 million respectably.. a What is the Sharpe ratio ( ERim)=Rg) of the market portfolio?. 1 b Other things being equal, describe what happens to the above Sharpe ratio increases or de- creases?) if the correlation coefficient between stock 1 and 2 is increased? Explain graphically. (use mean-standard deviation plane) c Other things being equal, describe what happens to the above Sharpe ratio increases or decreases?) if the risk-free asset is 6% (increased by 1%)? Explain graphically. (use mean- standard deviation plane)
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Answer to Part -A:-
Computation of Share Ratio :-
Calculation of Protfolio Return;-
| Stock | Amount(in million) | Weight | Ret | WTd Ret |
| Stock 1 | 3 | 0.75 | 20% | 15% |
| Stock 2 | 1 | 0.25 | 10% | 3% |
| 4.00 | 17.50% |
Calculation of Portfolio SD :-
| Particulars | Amount |
| Weight in A | 0.7500 |
| Weight in B | 0.2500 |
| SD of A | 20.00% |
| SD of B | 20.00% |
| r(A,B) | 0 |
| Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(A,B)] | |
| =SQRT[((0.75*0.2)^2)+((0.25*0.2)^2)+2*(0.75*0.2)*(0.25*0.2)*0] | |
| =SQRT[((0.15)^2)+((0.05)^2)+2*(0.15)*(0.05)*0] | |
| =SQRT[0.025] | |
| 15.81% |
| Sharpe Ratio: |
| Sharpe ratio = [ Expected Ret - Rf ] / SD |
| Rf - Risk free Ret |
| Particulars | Amount |
| Expected Ret | 17.50% |
| Risk Free Ret | 5% |
| SD | 15.81% |
| Sharpe ratio = [ Expected Ret - Rf ] / SD | |
| = [ 17.5 % - 5 % ] / 15.81 % | |
| = [ 12.5 % ] / 15.81 % | |
| = 0.7906 |
Therefore Sharpe Ratio will be 0.7906
Part -B
If there are is increase in the Correlation Co-efficient then Sharpe ratio will decrease
Because there is Direct reationship between SD and Correlation Coefficient that means if there is any increase in Correlation coefficient then SD will also increase but there is inverse relationship between SD abd Sharpe Ratio that menas if there is increase in SD then there will be decrease in Sharpe ratio.
Hence Increase in correlation Coefficient will lead to decrease in Sharpe ratio.
Part -C:-
if there is Increase in risk free rate then Share ratio will Decrease
As there is Inverese relationship between the sharpe ratio and Risk Free rate. Hence there is a Decrease in sharpe ratio if there is increase in Risk free rate.
