For a diversified portfolio including a large number of stocks: А. the weighted average of the betas goes to zero. В. the weighted average of unsystematic risks goes to zero. С. the weighted average of expected returns goes to zero. D. the return of the portfolio goes to zero.
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- ANSWER C AND D PLEASE ONLY Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) / n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w. c) Does the investor put more or less of his portfolio into the risky assetas his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How doesα change with wealth?Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w.Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.1) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?2) Find A as a function of w.
- Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?Consider the expected return and standard deviation of the following two assets: Asset 1: E[r1]=0.1 and s1=0.2 Asset 2: E[r2]=0.3 and s2=0.4 (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) r12=-1, (ii) r12=0. (b) Suppose r12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio? (c) Derive the formula for the variance of a portfolio with four assets.a) Explain the practical relevance of the mean-variance model of portfolio selection
- Assume that you manage a risky portfolio with an expected return of18% and a standard deviation of 28%. The T-note rate is 2.7%. If your client chooses to invest 75% of a portfolio in your fund and 25% in a T-note bond fund. a. What is the expected return of your client's portfolio? b. What is the standard deviation of your client's prtfolio?The market risk premium is 8 percent and the risk-free rate is 5 percent. Which stock has the most systematic risk? Which one has the most unsystematic risk? Which stock is “riskier”? Explain.Suppose the expected return on the tangent portfolio is 12% and its volatility is 30%.The risk-free rate is 3%.(a) What is the equation of the Capital Market Line (CML)?(b) What is the standard deviation of an efficient portfolio whose expected return of16.5%? How would you allocate $3,000 to achieve this position
- True or False: Increasing the number of stocks in a portfolio reduces firm-specific risk. TrueFalseConsider two stock portfolios. Portfolio A consists of 20 different stocks from firms in different industries. Portfolio B consists of four different stocks, also from firms in different industries. The return on Portfolio A is likely to be volatile than that of Portfolio B.Suppose a stock analyst recommends buying stock in the following companies:Company IndustryToyonda AutomotiveSaalvo AutomotiveGMW AutomotiveHonsubishi AutomotiveShexxon Oil and gasMobron Oil and gasAiring AircraftBoebus AircraftGoohoo TechnologyPherk PharmaceuticalEach of the following portfolios contains four of the stock picks. Which portfolio is the least diversified? Pherk, Airing, Goohoo, ShexxonToyonda, Honsubishi, Boebus, AiringToyonda, Saalvo, GMW, HonsubishiBoebus, Airing, Shexxon, MobronWhich statement about portfolio diversification is CORRECT? i) Typically, as more securities are added to a portfolio, total risk would be expected to decrease at an increasing rate.ii) Proper diversification can reduce or eliminate total risk.iii) The risk-reducing benefits of diversification do not occur meaningfully until at least 50-60 individual securities have been purchased.iv) Because diversification reduces a portfolio's total risk, it necessarily reduces the portfolio's expected return.Portfolios A, B, and C all lie on the efficient frontier that allows for risk-free borrowing and lending. Portfolio A and B have the following expected returns and return variances: A: μ_A=0.0925 , σ_A^2=0.0225 ; B: μ_B=0.11 , σ_B^2=0.04. Portfolio C’s return has variance σ_C^2=0.1225. What is the expected return and Sharpe ratio of Portfolio C? What is the risk-free interest rate? Explain your calculations
