10. If investors can freely trade assets in financial markets, then the impact of trading activity on expected returns insures that: I. all assets will have the same degree of total risk II. systematic risk can be diversified away III. all assets will have the same expected returns IV. all assets will have the same reward to risk ratio V. all assets will have the same risk premium 1. I only 2. II and III 3. IV only 4. III and IV 5. III, IV and V
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Part 2: Investment Allocations An investor has selected the following asset types in his portfolio. The expected return for each asset type has been estimated by using the historical data: Expected Returns Bonds 7% High tech stocks 12% Foreign stocks 11% Call options 14% Put options 14% Gold 9% Table 5: Expected returns of Investments The following table indicates the covariance matrix of the assets’ returns. Each diagonal entry is the variance of an asset and non-diagonal entries are the covariances between any pairs of assets. Bonds High tech stocks Foreign stocks Call options Put options Gold Bonds 0.001 0.0003 -0.0003 0.00035 -0.00035 0.0004 High tech stocks 0.009 0.0004 0.0016 -0.0016 0.0006 Foreign stocks 0.008 0.0015 -0.0055 -0.0007 Call options 0.012 -0.0005 0.0008 Put options 0.012 -0.0008 Gold 0.005 Table 6: The Covariance matrix of assets’ returns (i) Suppose that our investor wishes to invest $10,000 in this portfolio. Determine how he should allocate this investment to the individual assets in his portfolio in order to have a minimum baseline expected return of 11%, and at the same time, at a minimum risk. (ii) Let the solution pair be denoted by (r, e), where “r” denotes the minimized risk and “e” denotes the expected portfolio return after the problem is solved. Use successive values of 10%, 10.5%, 11%, 11.5%, 12%, 12.5%, 13% and 13.5% as the baseline return values to obtain eight pairs of solutions (r, e). Plot “e” versus “r”. Explain whether there exists a pattern in this plot. In other words, explain, in your opinion, the type of mathematical relationship that “r” and “e” may have.
Aishwarya K.
a) You currently have all of your ÂŁ1,000,000 wealth invested in an aggressive portfolio of UK stocks which has a beta of 1.3. You are concerned that this is too risky a position. You can also invest (both long and short) in a defensive UK stock portfolio which has a beta of exactly 0.3. You wish to reallocate your wealth so that some is invested in the aggressive portfolio and the rest in the defensive portfolio and so that your overall beta is 0.5. What are your portfolio weights on the aggressive asset and the defensive asset? (10 marks) b) A market consists of only two stocks, X and Y. The market cap of X is $3bn and that of Y is $7bn. X has an expected return of 10% and a return standard deviation of 32%. Y has an expected return of 8% and a standard deviation of 20%. Their return correlation is 0.25. i) What is the expected return on the market and the return standard deviation of the market? (10 marks) ii) What are the CAPM betas of X and Y? (10 marks) c) Assume that you believe in the Capital Asset Pricing Model. You believe that you have, through extensive research, identified a stock that plots below the Security Market Line. What does this imply for whether or not it is fairly priced? How would you exploit this situation? [Write no more than 5 sentences in your answer.] (10 marks)
Akash M.
A risk-averse investor can borrow or lend at a risk-free rate of 3%. Which of the following risky portfolios would the investor combine with the risk-free asset to maximise their utility? a. Portfolio C: Expected return = 6%, Standard Deviation = 10% b. Portfolio A: Expected return = 4%, Standard Deviation = 3% c. More information is required d. Portfolio B: Expected return = 5%, Standard Deviation = 7% Which of the following is a benefit of diversification? a. Systematic risk is generally reduced as you add more stocks to your portfolio b. All choices are TRUE c. Total risk is generally reduced as you add more stocks to your portfolio d. Returns generally increase as you add more stocks to your portfolio Which of the following asset allocations would be most appropriate for an investor who is 28 years old and works full-time? a. Listed Equity = 50%, Fixed Income = 20%, Cash = 5%, Property = 25% b. Listed Equity = 10%, Fixed Income = 5%, Cash = 80%, Property = 5% c. Listed Equity = 100%, Fixed Income = 0%, Cash = 0%, Property = 0% d. Listed Equity = 20%, Fixed Income = 40%, Cash = 20%, Property = 20% Four assets, A, B, C and D have the following risk and return. Return(A) = 5%, Risk(A) = 5%, Return(B) = 8%, Risk(B) = 5%, Return(C) = 5%, Risk(C) = 4%, Return(D) = 8%, Risk(D) = 6%. Which of the following statements about preferences for a risk-averse investor are correct? a. B is preferred to A, B is preferred to D, C is preferred to A b. B is preferred to D, C is preferred to A, D is preferred to C c. B is preferred to A, C is preferred to D, D is preferred to A d. B is preferred to C, B is preferred to D, C is preferred to A Consider three assets, HVN, QAN and RIO. All three assets have the same correlation with each other of 0.1. HVN has an expected return of 5% and a standard deviation of 6%. QAN has an expected return of 7% and a standard deviation of 8%. RIO has an expected return of 8% and a standard deviation of 10%. Which of the following combinations of stocks will provide the best risk-return outcome for a risk-averse investor? a. RIO and HVN b. RIO c. RIO and QAN d. RIO, QAN and HVN
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