Find how many times the market variance is of the SD of a portfolio half in the riskfree security and half in the market.
The market variance is .25 times (.5 x .5 = .25).
Is my answer correct?
Your answer is incorrect. To find how many times the market variance is of the standard deviation (SD) of a portfolio half in the risk-free security and half in the market, we need to follow a few steps:
Step 1: Find the SD of the portfolio
The formula for the SD of a portfolio is given by:
SD portfolio = √(weight of asset A * SD of asset A)^2 + (weight of asset B * SD of asset B)^2 + (2 * weight of asset A * weight of asset B * correlation)
In this case, we have two assets: the risk-free security and the market. Let's assume the SD of the risk-free security is SD_rf and the SD of the market is SD_m. The weights for both assets are 0.5 each.
Step 2: Calculate the correlation between the risk-free security and the market
The correlation coefficient measures the relationship between two assets' returns. It ranges between -1 and +1. In this case, the risk-free security is unaffected by the market, so the correlation is 0.
Step 3: Substitute the values into the formula
SD_portfolio = √((0.5 * SD_rf)^2 + (0.5 * SD_m)^2 + (2 * 0.5 * 0.5 * 0))
SD_portfolio = √(0.25 * SD_rf^2 + 0.25 * SD_m^2 + 0)
SD_portfolio = √(0.25 * (SD_rf^2 + SD_m^2))
Step 4: Find how many times the market variance is of the SD of the portfolio
Market Variance = 0.25 * (SD_m^2)
Number of times = SD_portfolio / Market Variance
Now, you need to substitute the values of SD_rf and SD_m into the formula to calculate the SD of the portfolio and find the number of times the market variance is of the SD of the portfolio.