Investment and Risk Management 022-2023 Tutorial solutions – Portfolio Risk and Return

Investment and Risk Management 2022-2023
Tutorial 4 solutions – Portfolio Risk and Return

1. 
   −10.1% is the holding period return, which is calculated as: (3,050 − 3,450 + 51.55)/3,450, which is c omprised of a dividend yield of 1.49% = 51.55/(3,450) and a capital loss yield of −11.59% = –400/(3,450).
   

2. 
   
   

3. 
   
   

4. 
   The geometric mean return compounds the returns instead of the amount invested.
   

5. 
   The annualized rate of return for ETF 2 is 12.05% = (1.0110^52/5) − 1, which is greater than the annualized rate of ETF 1, 11.93% = (1.0461^365/146) − 1, and ETF 3, 11.32% = (1.1435^12/15) − 1. Despite having the lowest value for the periodic rate, ETF 2 has the highest annualized rate of return because of the reinvestment rate assumption and the compounding of the periodic rate.
   

6. 
   A is correct. The asset’s returns are not used to calculate the portfolio’s variance [only the assets’ weights, standard deviations (or variances), and covariances (or correlations) are used].
   

7. 
   

8. 
   

9. (1 + 0.080)/(1 + 0.0210) = 5.8%
10. (1 + 0.065)/(1 + 0.0210) = 4.3%
11. (1 + 0.080)/(1 + 0.0250) = 5.4%
12. (1 + 0.0650)/(1 + 0.0250) = 3.9%
13. C is correct. Brokerage commissions are negotiated with the brokerage firm. A security’s liquidity impacts the operational efficiency of trading costs. Specifically, liquidity impacts the bid–ask spread and can impact the stock price (if the ability to sell the stock is impaired by the uncertainty associated with being able to sell the stock).
14. C is correct. Historical data over long periods of time indicate that there exists a positive risk–return relationship, which is a reflection of an investor’s risk aversion.
15. A is correct. A risk-free asset has a variance of zero and is not dependent on whether the investor is risk neutral, risk seeking or risk averse. That is, given that the utility function of an investment is expressed as , where A is the measure of risk aversion, then the sign of A is irrelevant if the variance is zero (like that of a risk-free asset).
16. C is correct. The most risk-averse investor has the indifference curve with the greatest slope.
17. A is correct. A negative value in the given utility function indicates that the investor is a risk seeker.
18. Investment 3 has the highest rate of return. Risk is irrelevant to a risk-neutral investor, who would have a measure of risk aversion equal to 0. Given the utility function, the risk-neutral investor would obtain the greatest amount of utility from Investment 3.