Consider the following two investments. One is a risk-free investment with a $100 return. The other investment pays $2,000 20% of the time and a $375 loss the rest of the time. Based on this information, answer the following:
(i) Compute the expected returns and standard deviations on these two investments individually. (ii) Compute the value at risk for each investment.
(iii) Which investment will risk-averse investors prefer, if either? Which investment will risk- neutral investors prefer, if either?
(i) Risk-free investment:
Expected return: $100
Standard deviation: Zero, because the return is certain
Risky Investment:
Expected return = (0.2 * $2000) + (0.8 * -$375) = $100
Standard Deviation = square root of [{0.2*(2000-100)^2} + {0.8*(-375-100)^2}]
= square root of [{0.2*3610,000} + {0.8*225,625}]
= square root of [{722,000 + 180,500}]
= square root of 902,500
= square root of 950
(ii) Risk-free investment:
Value at risk: $100 because it ensures a to pay a specified return
Risky Investment:
Value at risk: -$375 because it is maximum money which the investor may lose
(iii) The risk-free investment will be preferred by risk-averse investor. The risk-neutral investor will not hold any preference among two investments as they pay the similar expected return
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