The returns to a portfolio over the last 7 years are: Year Portfolio Returns 1 3% 2 2% 3 3% 12% 4 5 4% 17 6 8% 10% The risk-free rate is 2.26% per year. Calculate the Sortino ratio. Note, this question asks for the Sortino and not the Sharpe ratio. Enter your answer as a number rather than a percentage. That is, if your answer is 0.92, then enter 0.92 rather than 92%.

Assume that you are given the following historical returns for the Market and Security J. Also assume that the expected risk-free rate for the coming year is 4.0 percent, while the expected market risk premium is 15.0 percent. Given this information, determine the required rate of return for Security J for the coming year, using CAPM. Year 1 2 O21.20% 3 4 5 6 O22.34% O 23.49% O24.63% O24.10% Market 10.00% 12.00% 16.00% 14.00% 12.00% 10.00% Security J 12.00% 14.00% 18.00% 22.00% 18.00% 14.00%

Suppose the next month rate of return on a portfolio (worth $1M) is distributed as follows. Return Rate -0.05 -0.03 -0.01 0.00 0.01 0.03 0.04 0.07 0.10 0.12 Probability  1%    1.5% 2.5% 5% 10%  20%   25%   20%   10%  5%   What is the expected rate of return given that the return is known to be greater than or equal to 4%?

Consider an investment whose annual return is normally distributed with a mean of 6% and a standard deviation of 14%. (a) What is the probability that I lose money on this investment, in any given year? Please express your answer as a percentage, to the nearest ten basis points. Probability of Losing Money = (b) What is the 10% value at risk on the investment? Please express your answer as a percentage, to the nearest ten basis points. VaR 0.1 = % % (c) If I invest in this asset, how much should expect to lose in my worst year out of 10? Please express your answer as a percent, to the nearest ten basis points. %

I. Consider the following information about K oll and Nell for one-time period: Suppose that the correlation coefficient between the returns for Koll and Nell is -0.40'. If you invest 30% in Koll and 70% in Nell, what are the expected return and standard deviation of the portfolio? Interpret your results. II. The investor achieved the following annual rate of returns over the last four-year period: 25% in Y1, 15% in Y2, 20% in Y3, 10% in Y4. (a) Calculate the geometric average rate of return for the whole 4 year period. (b) Calculate the logarithmic average rate of return for the whole 4 year period.  III. Suppose you have a portfolio of IBM and Dell with a beta of 0.4 and 1.1, respectively. If you put 40% of your money in IBM, 55% in Dell and 5% in the risk-free asset, calculate and interpret the beta of your portfolio.  IV. Suppose that the beta value for Kei is 1.5, and the risk-free rate of interest is 4%. The investor wishes to (i) have a shareholding in only one company, Kei, and…

The risk-free rate is currently 8.1%. Use the data in the accompanying table for the Fio family’s portfolio and the market portfolio during the year just ended to answer the questions that follow. Data Item Fio’s Portfolio Market Portfolio Rate of return 12.8% 11.2% Standard deviation of return 15.5% 9.6% Beta 1.10 1.00 Calculate Sharpe’s measure for the portfolio and the market. Compare the two measures, and assess the performance of the Fios’ portfolio during the year ended. Calculate Treynor’s measure for the portfolio and the market. Compare the two measures, and assess the performance of the Fios’ portfolio during the year ended. Calculate Jensen’s measure. Use it to assess the performance of the Fio’s portfolio during the just ended.

For the upcoming year, the risk-free rate is 2 percent, and the expected return to the market is 7 percent. You are also given the following covariance matrix for Securities J,K, andL. \table[[Covariance,Security J,Security K,Security L],[Security J,0.0012532,0.0010344,0.0019711],[Security K,0.0010344,0.0023717,0.0013558],[Security L,0.0019711,0.0013558,0.0048442]] Also assume that you form a portfolio by putting 0 percent of your funds in Security J, 40 percent of your funds in Security K, and 60 percent of your funds in Security L. Based on this information, determine the standard deviation of the resulting portfolio. ◻ 6.47% 5.27% 4.98% 5.82% 4.77%

You had the following rates of return for on your portfolio for the last four years: 2016:  -12.3%2017:  18.4%2018:    5.0%2019:   12.5%Calculate the geometric average return on your portfolio.  Enter your answer as a decimal, rounded to four decimal places.

Remember, the expected value of a probability distribution is a statistical measure of the average (mean) value expected to occur during all possible circumstances. To compute an asset's expected return under a range of possible circumstances (or states of nature), multiply the anticipated return expected to result during each state of nature by its probability of occurrence. Consider the following case: Aaron owns a two-stock portfolio that invests in Happy Dog Soap Company (HDS) and Black Sheep Broadcasting (BSB). Three-quarters of Aaron's portfolio value consists of HDS's shares, and the balance consists of BSB's shares. Each stock's expected return for the next year will depend on forecasted market conditions. The expected returns from the stocks in different market conditions are detailed in the following table: Market Condition Probability of Occurrence 0.20 0.35 0.45 Strong Normal Weak Happy Dog Soap 17.5% 10.5% -14% • The expected rate of return on Happy Dog Soap's stock over…

An investor has an investment that has produced the following returns: Year 1: 10%, Year 2: 5%, Year 3: -7%, Year 4: -3%, Year 5: 12%. Calculate the arithmetic mean return on this investment. O 6.75 O 17.00 3.40 8.50