In: Finance
You expect the following set of possible outcomes for a stock:
Outcome | Probability | Ending Stock Price | Holding Period Return (Percent) | Risk-free rate (Percent) |
Good | 35% | $120 | 44.5 | 4 |
Neutral | 30% | $100 | 14 | 2 |
Bad | 35% | $70 | -16.5 | .5 |
What is the standard deviation of the risk-free rate? Please enter your answer in percent rounded to the nearest basis point.
X = Expected Risk free rate = Σ ( Probability * Risk free rate)
= (35% * 4%) + (30% * 2%) + (35% * 0.5%)
= 1.4% + 0.6% + 0.175%
= 2.175%
Variance of Risk free rate = Σ * Probability * (x - X)^2
= [35% * (4% - 2.175%)^2] + [30% * (2% - 2.175%)^2] + [35% * (0.5% - 2.175%)^2]
= [0.35 * 0.0003330625] + [0.30 * 0.0000030625] + [0.35 * 0.0004683437]
= 0.00011657187 + 0.00000091875 + 0.00016392029
= 0.00028141091
Standard Deviation of Risk free rate = Square root of Variance
= (0.00028141091)^(1/2)
= 0.01677530655
= 1.68%
Therefore, Standard deviation of risk free rate is 1.68%