If the market risk decreases, while everything else stays the same, then Select one: O A. the budget line of the portfolio parallelly moves up. B. the budget line of the portfolio does not change. Ос. the budget line of the portfolio becomes flatter. O D. the budget line of the portfolio becomes steeper.
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- Which 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.3. The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standard deviation of 20%. Answer the following questions. (a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition of A to make the investors prefer the optimal risky portfolio than the risk free asset? (b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expected return and standard deviation of the investor’s optimal complete portfolio?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 risk-averse investor will: a. Always accept a greater risk with a greater expected return b. Only invest in assets providing certain returns c. Sometimes accept a lower expected return if it means less ri d. Never accept lower risk if it means accepting a lower expected returnExplain how a given investor chooses an optimal portfolio. Will this choice always be a diversified portfolio, or could it be a single asset? Explain your answer based on the utility curves and the efficient frontier.For a given option portfolio, you are long vega (value increases as volatility goes up), and short theta (as time passes your options portfolio loses money). Are you net long or short options? Net long, because as volatility goes up and it increases in value and as time passes you lose value. Net short, because as volatility goes up and it decreases in value and as time passes you increase value. not consistent you are long one and short the other, so can't tell completely independent derivatives, its apples and oranges and no reflection on your portfolio
- The value of Jon’s stock portfolio is given by the function v(t) = 50 + 77t + 3t2, where v is the value of the portfolio in hundreds of dollars and t is the time in months. How much money did Jon start with? (y-intercept) What is the minimum value of Jon’s portfolio? (vertex)An investor is considering three strategies for a $1,000 investment. The probable returns are estimated as follows: • Strategy 1: A profit of $10,000 with probability 0.15 and a loss of $1,000 with probability 0.85 • Strategy 2: A profit of $1,000 with probability 0.50, a profit of $500 with probability 0.30, and a loss of $500 with probability 0.20 • Strategy 3: A certain profit of $400 Which strategy has the highest expected profit? Explain why you would or would not advise the investor to adopt this strategy.A moderately risk-averse investor has 50% of her portfolio invested in stocks and 50% in risk-free Treasury bills. Show how each of the following events will affect the investor’s budget line and proportion of stocks in her portfolio: A. The standard deviation of the return on the stock market increases, but the expected return on the stock market remains the same. B. The expected return on the stock market increases, but the standard deviation of the stock market remains the same. C. The return on risk-free Treasury bills increases.
- 3) A risk-loving individual has $1000 to invest. The individual maximizes his/her expected utility and has a monotonic utility function. Show that he/she will never choose a diversified portfolio - that is, show that he/she will either keep the entire $1000 in a safe, or invest the entire $1000 in a risky assesst, for which each $1 invested yields $] with probability p, and SB with probability (1-p), where $B<$1<$J.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 positionSuppose Caroline is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds.CombinationFraction of Portfolio in Diversified StocksAverage Annual ReturnStandard Deviation of Portfolio Return (Risk)(Percent)(Percent)(Percent)A 0 1.50 0B 25 3.00 5C 50 4.50 10D 75 6.00 15E 100 7.50 20There is a relationship between the risk of Caroline's portfolio and its average annual return.Suppose Caroline currently allocates 75% of her portfolio to a diversified group of stocks and 25% of her portfolio to risk-free bonds; that is, she chooses combination D. She wants to reduce the level of risk associated with her portfolio from a standard deviation of 15 to a standard deviation of 5. In order to do so, she must do which of the following? Check all that apply. Sell some of her stocks and use the proceeds to purchase…