question archive a) Assuming that the risk (standard deviation) of the market is 20 percent, calculate the beta for the following assets: - A short-term U
a) Assuming that the risk (standard deviation) of the market is 20 percent, calculate the beta for the following assets: - A short-term U
Subject:FinancePrice:2.86 Bought20
a) Assuming that the risk (standard deviation) of the market is 20 percent, calculate the beta for the following assets:
- A short-term U.S. Treasury bill
- Gold, which has a standard deviation equal to the standard deviation of the market but a zero correlation with the market
- A new emerging market that is not currently included in the definition of “market”—the emerging market’s standard deviation is 50 percent, and the correlation with the market is -0.15
- An initial public offering or new issue of stock with a standard deviation of 35 percent and a correlation with the market of 0.6 (IPOs are usually very risky but have a relatively low correlation with the market)
b. Suppose an investor allocates 10% of her wealth to T-bills, another 20% to gold, 30% to the emerging market and the rest to the initial public offering. If the expected market return is 13% and the risk-free rate is 4%, calculate the expected return of the investor's portfolio.
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A) Beta of a risk free security is 0. Since US treasury bill is a sovereign security it is assumed to be risk free and hence its Beta will be 0.
B) Beta of a secuity can be calculated using formula if we have Standard deviation of both market and security and Correlation of security with market available -
Beta of Security = rAX * SDA/SDX
Since there is no correlation between Gold and Market r becomes 0 and hence beta also becomes 0.
C) Beta of Market is always 1. But since it is not included in definition of market we havee to use formula used in B) to calculate Beta
Beta = -0.15 * 0.5/0.2
= -0.375
D) We can use same Formula as given in B) above
Beta = 0.6 * 0.35/0.20
= 1.05
Beta of a portfolio is weighted average of individual beta of security in portfolio
So, beta of portfolio given in question becomes
= 0 * 10% + 0 * 20 % + (-0.375* 30%) + 1.05* 40%
= 0.3075
As per CAPM ,
Return = Risk free rate + ( Market return - Risk free) *Beta
= 4 + ( 13 - 4) * 0.3075
= 6.7675%
