Suppose the utility function is U = E(r) - 0.5Ao2. Draw the indifference curve corresponding to a utility level of 0.2 for an investor with a risk aversion coefficient of 3. Please note the vertical line indicates expected return, and plot standard deviation on the horizontal line.
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Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
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- What must be true about the sign of the risk aversion coefficient, A, for a risk lover? Draw the indifference curve for a utility level of .05 for a risk lover.Consider the following linear regression model: (R₁-r)= a; + b(RMkt - rf) + e; The b; in the regression: O measures the deviation from the best fitting line and is zero on aver- measures the sensitivity of the security to market risk. measures the diversifiable risk in returns.Draw the indifference curve in the expected return–standard deviation plane corresponding to a utility level of .05 for an investor with a risk aversion coefficient of 3. (Hint: Choose several possible standard deviations, ranging from 0 to .25, and find the expected rates of return providing a utility level of .05. Then plot the expected return–standard deviation points so derived.)
- Mean-variance expected utility is given by Eu = e-, where e is expected return, v is the variance of the portfolio and tis risk tolerance. Suppose an investor has risk-loving preferences. What can we say about the value of t? Select one: Ot1 O. t>0 O t=0On the basis of the utility formula below, which investment would you select if you were risk averse with A = 4? Investment Expected return E(r) Standard deviation σ 1 0.12 0.30 2 0.15 0.50 3 0.21 0.16 4 0.24 0.21a) Discuss the difference between a price-weighted index and a value-weighted index. Give one example for the price-weighted index and one example for the value-weighted index and discuss any problems/advantages associated with the specific indices. b) We assume that investors use mean-variance utility: U = E(r) – 0.5 × Ao², where E(r) is the expected return, A is the risk aversion coefficient and o? is the variance of returns. Given that the optimal proportion of the risky asset in the complete port- folio is given by the equation y* = E , where r; is the risk-free rate, E(rp) is the expected returm of the risky portfolio, o, is variance of returns, and A is the risk aversion coefficient. For each of the variables on the right side of the equation, discuss the impact of the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse. Ao
- Consider two assets. Suppose that the return on asset 1 has expected value 0.05 and standard deviation 0.1 and suppose that the return on asset 2 has expected value 0.02 and standard deviation 0.05. Suppose that the asset returns have correlation 0.4.Consider a portfolio placing weight w on asset 1 and weight 1-w on asset 2; let Rp denote the return on the portfolio. Find the mean and variance of Rp as a function of w.Which one of the following statements is correct? Multiple Choice The risk-free rate of return has a risk premium of 1.0. The reward for bearing risk is called the standard deviation. Risks and expected return are inversely related. The higher the expected rate of return, the wider the distribution of returns. Risk premiums are inversely related to the standard deviation of returns.There are two assets 1 and 2, with returns X and Y correspondingly. Return X is a random variable with mean 1 and variance 1; return Y is a random variable with mean 1 and variance 3. We know that the expectation of X*Y is equal to 0. Find the share of asset 1 in the risk-minimizing portfolio.
- Suppose you have mean-variance utility function with a coefficient of risk Aversion-0, which stocks are preferred to P. E(r) III IP II IV Standard DeviationYou are given the following data about Asset A and Asset B. Asset A Asset B Expected returns 8.6% 7.9% Standard Deviation 3.8% 4.6% Assuming that an investor is to choose between Asset A or Asset B, explain which asset a rational investor will choose. c) With the use of a diagram, explain why an investor will always choose a point on the SML line.Define the following terms: Factor risk premium Unit root Random walk with drift Standardized beta ARCH