Vasil Gerchev Professor Milind Shrikhande FI 4000 30 January 2023 Chapter 5 Problem Set 1 1 The first change that happens if inflation increases from 3 to 5 the nominal rate will increase by 2 while the real rate doesn t change The second deals with the nominal rate not changing when inflation is expected to increase That is when the real rate changes This means the real rate decreases as inflation increases 2 No because with the Sharpe ratio we are using numbers that are presented in nominal figures This means we should be using nominal data 3 I would decrease due to the fact that in most cases the standard deviation exceeds its return In order to gain back the risk return portfolio relationship the portfolio will need to decrease the number of risk free investments 4 Mean 0 3 44 0 4 14 0 3 16 0 3 0 4 0 3 Mean 0 14 Standard Deviation square root 0 3 44 14 2 0 4 14 14 2 0 3 16 14 2 1 Standard Deviation 23 23 5 expected return on portfolio 3 00 8 34 11 34 6 Required return on portfolio Risk free rate Risk premium 5 10 15 Value of the portfolio Present value of Expected cashflow 100 000 1 15 86 956 52 7 Expected return for equity fund T bill rate Risk premium 6 10 16 Expected rate of return of the client s portfolio 0 6 16 0 4 6 12 Expected return of the client s portfolio 0 12 100 000 12 000 Standard deviation of client s overall portfolio 0 6 14 8 4 8 Market Value of the portfolio Value 1 g n 100 000 1 05 7 140 710 04 Chapter 6 1 As long as the correlation coefficient is below 1 then the portfolio will benefit from diversification This is due to the returns on component securities not moving to the perfect lockstep This causes the standard deviation to be less than a weighted average of the standard deviation of the component securities 2 Since the expected return of the portfolio is the first item in the numerator of the Sharpe ratio the ratio will be changed The expected return of the portfolio will be impacted if the asset allocation is changed 3 After doing the work I got E R 10 therefore the risk free rate must be up to 10 This means the equilibrium can not be greater than 10 4 Investors will not arrive at the same optimal risky portfolio because every investor takes on a different amount of risk Some play it safer and others want a higher reward so they will take more risks The different expectations of various investors cause the portfolios of every investor to be different 5 In the special case that all assets are perfectly positively correlated the portfolio standard deviation is equal to the weighted average of the component asset standard deviations 6 E r 0 70 100 0 30 50 0 70 0 15 0 55 Standard Deviation 0 70 1 0 55 2 0 30 0 50 0 55 2 47 25 square root 47 25 68 74 7 Expected rate of return would be revised to 1 2 8 9 6 8 Risk Port for Stock 0 095 0 23 2 0 035 0 011 0 095 0 23 2 0 035 0 32 2 0 13 0 011 64 66 Risk Port for Bond 1 64 99 35 34 Expected Return 64 66 0 15 35 34 0 09 12 88 Standard Deviation sqrt 6466 2 0 32 2 3534 2 0 23 2 2 0 2285 0 011 23 34 Sharpe Ratio 0 1288 0 0550 0 2334 0 3162 or 31 62