Next year the economy will be in an expansion, normal, or recession state with probabilities 0.46, 0.39, and 0.15, respectively. The returns (%) on the securities in these states are as follows. Security 1 {+9.30, +9.30, +7.80}; Security 2{+15.60, +7.50, +2.20}; Security 3 {expansion = +13.57, normal = +9.20, recession = +4.60}. Your client will invest in one of these portfolios only. Which security can you rule out, that is, you will not advise your risk-averse client to invest in it?
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Next year the economy will be in an expansion, normal, or recession state with probabilities 0.46, 0.39, and 0.15, respectively. The returns (%) on the securities in these states are as follows. Security 1 {+9.30, +9.30, +7.80}; Security 2{+15.60, +7.50, +2.20}; Security 3 {expansion = +13.57, normal = +9.20, recession = +4.60}. Your client will invest in one of these portfolios only. Which security can you rule out, that is, you will not advise your risk-averse client to invest in it?
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- 2) Calculate the expected rate of return and standard deviation for a security with the following possible outcomes: State of the Economy Probability of State Return if State Occurs Depression 0.2 -5% Recession 0.4 3% Slow growth 0.3 7% Moderate growth 0.1 10%An Overview of Financial Management and the Financial Environment Differentiate between the following types of markets: physical asset vs. financial markets, spot vs. futures markets, money vs. capital markets, primary vs. secondary markets, and public vs. private markets the real risk free rate of interest is 3%. Inflation is expected to be 2% this year and 4% during the next 2 years. Assume that the maturity risk premium (MRP) is zero. What is the yield on a 2 year Treasury security? What is the yield on 3 year Treasury securities? If Apple Computer decided to issue additional common stock, and someone purchased 100 shares of this stock from Merrill Lynch, the underwriter, would this transaction be a primary market transaction or a secondary market transaction? Would it make a difference if the investor purchased previously outstanding Apple stock in the dealer market?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 own a portfolio with the following expected returns given the various states of the economy. What is the overall portfolio expected return? State of Economy Boom Normal Recession 0.0701 O 0.0648 0,0719 O 0.0548 Expected returns in various states of the economy Probability 0.0442 23.00% 70.00% 7.00% 13.00% 7.00% -10.00% Rate of ReturnSuppose your expectations regarding the stock market are as follows: State of the Economy Boom Normal growth Recession Probability 0.3 0.4 0.3 Mean Standard deviation E (r) Σ=1p(s)r(s) Var (r) = o² = Σ³-1 P (s)[r (s) — E (r)]² - SD (r) = o = √Var (r) Required: Use above equations to compute the mean and standard deviation of the HPR on stocks. (Do not round intermediate calculations. Round your answers to 2 decimal places.) 14.00% 23.24% HPR X 2 decimal places required. 44% 14 -16Consider the following information in Figure 1 below for a portfolio including security A and security B: Figure 1 State of the economy Probability of state of economy Return on A (%) Return on B (%) Boom 0.2 15 5 Growth 0.2 -5 0 Normal 0.5 10 10 Recession 0.1 5 20 If you want to include one more security C into the above portfolio. (e.g., a new portfolio including securities A, B, and C), what is the new portfolio variance if you invest 40% of C and 60% of the old portfolio including A and B (50% weights for A and B)? Assume the standard deviation of C is 10%, and correlation coefficient between the old portfolio and C is 0.8.
- You live in a world where three future states are possible: Boom, Normal and Recession. See the probablities of these states in the attched table. Consider a stock which you expected to have the following returns in these states of the economy. State Probability Boom Normal Recession O 9.05% O 7.35% What is the expected return on an investment in this stock? 6.00% 25% 55% 20% O 3.75% State Expected Return 0.15 0.08 -0.04Consider the following scenario analysis: Rate of Return Scenario Probability Stocks Bonds Recession 0.30 −5 % 18 % Normal economy 0.60 19 % 7 % Boom 0.10 24 % 7 % b. Calculate the expected rate of return and standard deviation for each investment.Consider two stocks, A and B, whose returns in a boom and a recession are given below. Stock A: recession (-15%), boom (+20%). Stock B: recession (+10%), boom (-2%). Suppose that there is a 10% chance of a recession next year. How would you allocate money between these two stocks so as to minimize your risk?
- Suppose the real risk-free rate is 4.05% and the future rate of inflation is expected to be constant at 2.00%. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is valid? Include cross-product terms, i.e., if averaging is required, use the geometric average. (Round your final answer to 2 decimal places.) a. 4.05% O b. 2.08% O c. 6.05% O d. 6.13% O e. 4.13%Refer the table below on the average excess return of the U.S. equity market and the standard deviation of that excess return. Suppose that the U.S. market is your risky portfolio. Period 1927-2021 1927-1950 1951-1974 1975-1998 1999-2021 Average Annual Returns U.S. equity 12.17 10.26 10.21 17.97 10.16 1-Month T-Bills 3.30 0.93 3.59 6.98 1.66 U.S. Excess return 8.87 9.33 6.62 10.99 8.50 Equity Market Standard Deviation 20.25 26.57 20.32 14.40 18.85 Sharpe Ratio 0.44 0.35 0.33 0.76 0.45 Required: a. If your risk-aversion coefficient is A = 4.9 and you believe that the entire 1927-2021 period is representative of future expected performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility function is u = E(r) 0.5 × Ao². b. What if you believe that the 1975-1998 period is representative?Assume that the risk-free rate, RF, is currently 8%, the market return, RM, is 12%, and asset A has a beta, of 1.10. (could be done on word document or excel). Assume that as a result of recent economic events, inflationary expectations have declined by 3%, lowering RF and RM to 5% and 9%, respectively. Draw the new SML on the axes in part a, and calculate and show the new required return for asset A. Assume that as a result of recent events, investors have become more risk averse, causing the market return to rise by 2%, to be14%. Ignoring the shift in part c, draw the new SML on the same set of axes that you used before, and calculate and show the new required return for asset A. From the previous changes, what conclusions can be drawn about the impact of (1) decreased inflationary expectations and (2) increased risk aversion on the required returns of risky assets?