What is the standard deviation of the risk-free rate?

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.

Solutions

Expert Solution

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%

jeff jeffy answered 2 years ago

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