Marcus has an investment portfolio that paid the rate of return of 24.75%, -11%, - 30%, 19%, 15.5%, 12% and 20% over the last seven (7) years. Required: a) Calculate the arithmetic average return and the geometric average return of
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Marcus has an investment portfolio that paid the
Required:
-
a) Calculate the arithmetic average return and the geometric average return of this
portfolio.
-
b) Discuss the difference between arithmetic average return and the geometric
average return. When should Marcus use a specific average return?
-
c) If the following information is available for Marcus’s portfolio in the
forecast for next year, calculate the expected return and identify the risk of return by computing the variance and the standard deviation.
State of economy
Boom Normal Recession
Question 5
Probability of the economic state
0.55 0.30 0.15
Rate of Return
25% 17% -8%
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- The following table reports the percentage of stocks in a portfolio for nine quarters: a. Construct a time series plot. What type of pattern exists in the data? b. Use trial and error to find a value of the exponential smoothing coefficient that results in a relatively small MSE. c. Using the exponential smoothing model you developed in part (b), what is the forecast of the percentage of stocks in a typical portfolio for the second quarter of year 3?Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the general economic conditions are improving, stable, or declining. The anticipated annual return percentages for each market segment under each economic condition are as follows: Assume that an individual investor wants to select one market segment for a new investment. A forecast shows improving to declining economic conditions with the following probabilities: improving (0.2), stable (0.5), and declining (0.3). What is the preferred market segment for the investor, and what is the expected return percentage? At a later date, a revised forecast shows a potential for an improvement in economic conditions. New probabilities are as follows: improving (0.4), stable (0.4), and declining (0.2). What is the preferred market segment for the investor based on these new probabilities? What is the expected return percentage?Leon has in his investment a portfolio that paid him the rate of returns of 14 %, -13%, 15.6%, 17% and 19.5% over the past five years. Required: a)Calculate the arithmetic average return (AAR) and geometric average return (GAR) of the portfolio? If someone asks you what is the actual compounding rate of return of Leon’s portfolio over the past five year, which one (AAR or GAR) will be a better answer? b)Following is forecast for economic situation and Leon’s portfolio returns next year, calculate the expected return, variance and standard deviation of the portfolio. State of economy Probability Rate of returns Mild Recession 0.25 -2.5% Normal 0.45 13.5% Growth 0.30 20% c) Assume that expected return of the stock A in Leon’s portfolio is 13.2%. Beta of this stock is 1.2, risk free rate is 3.5%. Calculate market portfolio rate of return, which is used to compute the expected return of this stock by Capital Asset Pricing Model (CAPM)?
- You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 12 percent and 15 percent, respectively. The standard deviations of the assets are 29 percent and 48 percent, respectively. The correlation between the two assets is .25 and the risk-free rate is 5 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? What is the smallest expected loss for this portfolio over the coming year with a probability of 2.5 percent?Using the data in the following table, LOADING... , consider a portfolio that maintains a 75% weight on stock A and a 25% weight on stock B. a. What is the return each year of this portfolio? b. Based on your results from part (a), compute the average return and volatility of the portfolio. c. Show that (i) the average return of the portfolio is equal to the (weighted) average of the average returns of the two stocks, and (ii) the volatility of the portfolio equals the same result as from the calculation in Eq. 11.9. d. Explain why the portfolio has a lower volatility than the average volatility of the two stocks. Question content area bottom Part 1 a. What is the return each year of this portfolio? Enter the return of this portfolio for each year in the table below: (Round to two decimal places.) Year 2010 2011 2012 2013 2014 2015 Portfolio enter your response here% enter your response here% enter your response…Leon has in his investment a portfolio that paid him the rate of returns of 14 %, -13%, 15.6%, 17% and 19.5% over the past five years. Required: Calculate the arithmetic average return (AAR) and geometric average return (GAR) of the portfolio? If someone asks you what is the actual compounding rate of return of Leon’s portfolio over the past five year, which one (AAR or GAR) will be a better answer? (2 marks) Following is forecast for economic situation and Leon’s portfolio returns next year, calculate the expected return, variance and standard deviation of the portfolio. (4 marks) State of economy Probability Rate of returns Mild Recession 0.25 -2.5% Normal 0.45 13.5% Growth 0.30 20% c) Assume that expected return of the stock A in Leon’s portfolio is 13.2%. Beta of this stock is 1.2, risk free rate is 3.5%. Calculate market portfolio rate of return, which is used to compute the expected return of this stock by Capital Asset Pricing Model…
- David established an investment portfolio of two blue chips four years ago: Gold share and Silver Bond. Gold share accounts for 65% of his investment portfolio. Required: If David’s portfolio has provided the returns of 9.5%, 11.3%, - 12.5% and 15.6% over the past four years, respectively. Calculate geometric average return of the portfolio for this period? Assume that the below data is available for David’s portfolio performance, calculate the expected return, variance and standard deviation of the portfolio. Assume that expected return of the Gold share in David’s portfolio is 14.5%. The share’s beta coefficient is 1.5. Market risk premium is 7.5. Calculate the risk-free rate using Capital Asset Pricing Model Assume that David bought 2000 of Gold shares in his portfolio for a price of $75 each, the dividend paid for this stock is $7/stock each year. The current market price of this share is $135. Calculate the capital gain yield of this investment after four yearsI. 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…During a particular investment period, a wealth management company held an investment portfolio that earned an average return of 13% with standard deviation of 30% and beta of 1.5. The average risk-free rate of return during this investment period was 2%. (full process) (a) Calculate the Sharpe and Treynor measures of performance evaluation for this investment portfolio. This investment portfolio is composed of the following two asset classes: Asset Class Weight Return Equity 0.80 15% Bonds 0.20 5% During this particular investment period, the information on a benchmark portfolio is given in the following table. Asset Class Weight Return Equity (S&P500 Index) 0.50 17% Bonds (Lehman Brothers Index) 0.50 5% (b) Determine whether the investment portfolio of the wealth management company performed better than the benchmark portfolio in terms of the total…
- David established an investment portfolio of two blue chips four years ago: Gold share and Silver Bond. Gold share accounts for 65% of his investment portfolio. Required: If David’s portfolio has provided the returns of 9.5%, 11.3%, - 12.5% and 15.6% over the past four years, respectively. Calculate geometric average return of the portfolio for this period? Assume that the below data is available for David’s portfolio performance, calculate the expected return, variance and standard deviation of the portfolio. Gold Share Silver Bond Expected return 26.5% 10.5% Standard Deviation of return 6% 2% Correlation of coefficient (p) 0.55 Assume that expected return of the Gold share in David’s portfolio is 14.5%. The share’s beta coefficient is 1.5. Market risk premium is 7.5. Calculate the risk-free rate using Capital Asset Pricing Model Assume that David bought 2000 of Gold shares in his portfolio for a price of $75 each, the dividend paid for this…Talal can pick one of two investment portfolios - A and B. Each requires an initial outlay of $100,000 and each has a most likely annualrate of return of 18%. Estimated the returns associated with each investment. Past estimates indicate that the probabilities of thepessimistic, most likely, and optimistic outcomes are 30%, 50%, and 20%, respectively. Note that the sum of these probabilities mustequal 100%; that is, they must be based on all the alternatives considered.Question:1. Explain him about risk aversion, risk neutrality and risk seeking on the bases of standard deviation and coefficient of variation.DetailsAsset AAsset B1.Initial Investment$100.000$100,000Rate of Return - Pessimistic16%10%Rate of Return - Most likely18%18%Rate of Return - Optimistic20%26%A particular firm’s portfolio is composed of two assets, which we will call" A" and "B." Let X denote the annual rate of return from asset A, and let Y denote the annual rate of return from asset B. Suppose that E(X) = 0.15, E(Y) = 0.20, SD (X) = 0.05, SD (Y) = 0.06, and CORR (X, Y) = 0.30. Use a spreadsheet to perform the following analysis. (a) What is the expected return of investing 50% of the portfolio in asset A and 50% of the portfolio in asset B? What is the variance of this return? (b) Replace CORR (X, Y) = 0.30 by CORR (X, Y) = 0.60, 0, -0.30, and -0.60 and answer the questions in part (a). What is the impact of correlation on the expected returns and its variance? Explain why this is so. (c) Suppose that the fraction of the portfolio that is invested in asset B is f, and so the fraction of the portfolio that is invested in asset A is (1 – f). Let f vary from f = 0.0 to f = 1.0 in increments of 5% (that is, f = 0.0, 0.05, 0.10, 0.15, ...), and compute the mean and the…
