# Investment analysis

Anonymous

Question description

1. If you can answer the following questions I will send the data:

1)  Calculate the mean, standard deviation, skewness, and excess kurtosis of the returns on each portfolio. Comment on the degree to which these returns either appear or do not appear to be normally distributed. Calculate the annualized Sharpe Ratio for each portfolio.1 Assuming a long investment in one of these portfolios, do you see any reason to prefer the Sortino Ratio as a performance ratio over the Sharpe Ratio? Briefly discuss. If so, calculate the Sortino Ratio for each of these portfolios and annualize the estimates in the same way that you did for the Sharpe Ratio. Based only on either the Sharpe Ratio or the Sortino Ratio, which of these portfolios would you prefer to own and why?

2. 2)  Calculate Value at Risk and Expected Shortfall for each portfolio at the 5% and 1% levels

1. Assuming normality for the portfolio returns

2. Using the empirical method (i.e., making no distributional assumption about the

return generating process for each portfolio).

Compare your answers from parts (i) and (ii) above. What do these answers tell you about whether (or not) your portfolio’s returns appear to be normally distributed. Using your answers to part (ii), revisit your preferences over the three portfolios in problem (1) based only on their, respective, Sharpe or Sortino Ratio. Do you still maintain those same preferences? What (if anything) additional do you learn from your estimates in part (ii)?

3. 3)  Your VaR estimates from parts (i) and (ii) in problem (2) are based on 1,277 trading day returns. Over the next 1,277 trading days, how many times would you expect the actual portfolio returns to fall below these VaR estimates? Suppose for, say, the equal-weighted portfolio, over the next 1,277 trading days, the number of times that the actual portfolio return falls below your VaR estimate from part (i) in problem (2) at the 1% confidence level exceeds that expectation. What would you, then, conclude? Suppose, again, for the equal-weighted portfolio, the number of times over the next 1,277 trading days that the actual portfolio return falls below your VaR estimate from part (ii) in problem (2) at the 1% confidence level exceeds that expectation. What would you, then, conclude?

1 To do so, first calculate the given portfolio’s Sharpe Ratio assuming the risk-free rate to be approximately zero. Next, scale this estimate by √252, where 252 is the approximate number of trading days in a year.

2

In problems (4) and (5) below, briefly describe what you would do; you do not have to actually do it.

1. 4)  The Chief Risk Officer for the SMIF portfolio wants a sensitivity analysis performed on the expected shortfall estimate you calculated in part (ii) of problem (2)? Specifically, he (or she) took Investments and recalls the example from class where ES is estimated the day before and the day after the stock market crash of ’87. How might you conduct such a sensitivity analysis using more current events?

2. 5)  The Chief Risk Officer of the SMIF portfolio also wants to know what securities within the portfolio contribute the most to the portfolio’s Expected Shortfall estimate. How might you answer this question?

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