What is the Gamma of a portfolio of 100 long puts and how can we Delta-Gamma hedge with the following parameterization? ୮ 1 1 = e Soo√T √√2π (So = 100, K = 110, T = 2,σ = 0.10, r = 0.05)

Mrs Z's utility function is given by the following equation: Uz(R, o²) = 0.3R – 0.50? Find the overall optimal portfolio for Mrs Z and compute its expected return and the standard deviation of its 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.

4. Suppose that there are 2 assets with ri 012 = 0.005. = 0.20, 01 = = 0.40, 2 = 0.10, 02 = 0.25 and (a) If ro = 0.02, what are the market portfolio return and variance? What are the corre- sponding weights (i.e. how much to invest in asset 1, asset 2, and the risk-free asset to get the market portfolio)? Answer. (b) If ro 0.05, what are the market portfolio return and variance? What are the corre- sponding weights? Answer.

Use the following CAPM equation for a portfolio to answer the questions that follow:E(RP) = RF + βP (RM – RF) = 1 + 0.8 (5 – 1) = 4.2% a) Is the portfolio defensive or aggressive. Why? b) If the actual portfolio return is 6%, what is the portfolio’s alpha?

The beta of the risk-free asset is: 0.5 1.0 -1.0 2.0

Based on the following probability distribution, what is the security’s expected return? State         Probability                       r     1                 0.2                        –5.0% 2                 0.4                        10.0 3                 0.4                        30.0

Hi there, I am trying to figure out how to calculate 5 data points so I can plot the feasible set of portfolios for A, B and C on a graph. I am unsure of the process to calculate the data points.   ρ23 is +1.0 Thank you

Consider a single-index model economy. The index portfolio M has E(RM ) = 6%, σM = 18%.An individual asset i has an estimate of βi = 1.1 and σ2ei = 0.0225 using the single index modelRi = αi + βiRM + ei. The forecast of asset i’s return is E(ri) = 12%. rf = 4%. a) According to asset i’s return forecast, calculate αi.  (b) Calculate the optimal weight of combining asset i and the index portfolio M .  (c) Calculate the Sharpe ratio of the index portfolio M and the portfolio optimally combiningasset i and the index portfolio M .

On 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         0.21