Amy considers two investment opportunities (Stock A and Stock B) with the same price per unit in the market. The payoff per unit invested in Stock A and Stock B has the same distribution. Amy wants to buy Stock A and asks for opinions from her friend Tom, who is a financial advisor and knows Amy is risk averse. Tom suggests Amy should consider a portfolio comprising both of the stocks, rather than put all money on a single stock. Use the expected utility theory to explain Tom's suggestion.
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Expected utility theory in portfolio theory
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- Your client is shocked at how much risk Blandy stock has and would like to reduce the level of risk. You suggest that the client sell 25% of the Blandy stock and create a portfolio with 75% Blandy stock and 25% in the high-risk Gourmange stock. How do you suppose the client will react to replacing some of the Blandy stock with high-risk stock? Show the client what the proposed portfolio return would have been in each year of the sample. Then calculate the average return and standard deviation using the portfolios annual returns. How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation?Anita is comparing the common stocks of two companies. One of the measures she wants to use in her purchase decision is the stock’s beta value. One stock has a beta of 0.80, while the other has a beta of 0.60. If Anita wants to maximize her potential return, which company’s stock should she purchase? The company whose stock has the lower (0.60) beta. The company whose stock has the higher (0.80) beta.A close family friend has approached you to help her determine which of the two common stocks she should invest in Common Stock A Common Stock B Probability Return Probability Return 0.25 11% 0.25 -5% 0.15 15% 0.25 6% 0.6 19% 0.25 14% 0.25 22% Required: Calculate the expected returns of stock A Determine the risk (standard deviation) and return of stock A Calculate the expected returns of stock B Determine the risk (standard deviation) and return of stock B Which investment should your friend invest in? Jenny has decided that she will invest her $100,000 savings in stocks as follows: What rate of return should Jenny expects to receive on her portfolio? Company Percentage of Investment Expected rate of return Standards Company Limited 45% 9% Starbucks 15% 12% Treasury Bill 40% 4%
- JJ is a risk-averse investor, she cannot decide whether to invest in stock A or Stock B or in a portfolio that is a combination of both stocks. He has approached the bank and the company has provided her with the following information Probability (%) Expected return (%) Stock A Expected return (%) Stock B 30 13 15 20 14 13 20 15 12 30 16 11 Using these stocks, he has identified two investment portfolio alternatives: Alternative Portfolio 1 100% of A 2 30% of A and 60% of B Calculation the portfolio return and standard deviation for each alternativeChristy is considering investing in the common stock of One Liberty and Heico. The following data are available for these two securities: One Liberty Heico Expected return 0.12 0.16 Standard deviation of returns 0.08 0.20 If she invests 30% of her funds in Heico and 70% in One Liberty, and if the correlation of returns between these securities is +0.65, what is the portfolio's expected return and standard deviation?Clay Jensen is evaluating whether to purchase one of 2 different stocks and is considering the investment in isolation (he has no other investments). Clay believes stock A has equal probabilities of returning 6%, -10%, or 22%. He believes stock B has equal probabilities of returning 9%, -20%, or 35%. The risk-free rate is 4%. What is the appropriate measure to compare these two stocks and which investment should he choose?
- A close family friend has approached you to help her determine which of the two common stocks she should invest in. Common Stock A Common stock B Probability Return Probability Return 0.25 11% 0.25 -5% 0.15 15% 0.25 6% 0.6 19% 0.25 14% 0.25 22% Required: Calculate the expected returns of stock A Determine the risk (standard deviation) and return of stock A Calculate the expected returns of stock B Determine the risk (standard deviation) and return of stock B Which investment should your friend invest in?Ms. B has $1000 to invest. She is considering investing in the common stock of company M. In addition, Ms. B will either borrow or lend at the risk-free rate. Ms. B decide to invest $350 in common stock of company M and $650 placed in the risk- free asset. The relevant parameters are 1) What is the expected return? 2) What is the variance of the portfolio? 3) What is the standard deviation of the portfolio?Rachel is a financial investor who actively buys and sells in the securities market. Now she has a portfolio of all blue chips, including: $13,500 of Share A, $7,600 of Share B, $14,700 of Share C, and $5,500 of Share D. (a) Compute the weights of the assets in Rachel’s portfolio?(b) Find the geometric average return (c)Find the risk free rate of return (d)Find the expected rate of return of the portfolio
- You must choose between investing in Stock A or Stock B. You have already used CAPM to calculate the rate of return you should expect to receive for each stock given each one’s systematic risk and decided that the expected return for both exceeds that predicted by CAPM by the same amount. In other words, both are equally attractive investments for a diversified investor. However, since you are still in school and do not have a lot of money, your investment portfolio is not diversified. You have decided to invest in the stock that has the highest expected return per unit of total risk.If the expected return and standard deviation of returns for Stock A are 10 percent and 25 percent, respectively, and the expected return and standard deviation of returns for Stock B are 16 percent and 36 percent, respectively, which should you choose? Assume that the risk-free rate is 7 percent.Assume that a risk-averse investor owning stock in Miller Corporation decides to add the stock of either Mac or Green Corporation to her portfolio. All three stocks offer the same expected return and total variability. The correlation of return between Miller and Mac is −.05 and between Miller and Green is +.05. Portfolio risk is expected to:a. Decline more when the investor buys Mac.b. Decline more when the investor buys Green.c. Increase when either Mac or Green is bought.d. Decline or increase, depending on other factors.Fred holds a portfolio with a 21% volatility. He decides to short sell a small amount of stock with a 48% volatility and use the proceeds to invest more in his portfolio. If this transaction reduces the risk of his portfolio, what is the minimum possible correlation between the stock he shorted and his original portfolio?