Question

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 covariance of the stock holding period returns with the stock's ending price? Please enter your answer rounded to the third decimal place.

Answer 1

X = Expected Stock ending price = Σ ( Probability * Risk free rate)

= (35% * 120) + (30% * 100) + (35% * 70)

= $42 + $30 + $24.5

= $96.5

Y = Expected Holding period return = Σ ( Probability * Risk free rate)

= (35% *44.5%) + (30% * 14%) + (35% * -16.5%)

= 15.575% + 4.2% - 5.775%

= 14%

n = 3

Covariancve = Σ (x - X) * (y - Y) / n

= [[($120-$96.5) * (44.5%-14%)] + [($100 - $96.5)*(14%-14%)] + [($70 - $96.5)*(-16.5%-14%)]] / 3

= [($23.5 * 30.5%) + ($3.5*0) + ($26.5 * -30.5% )] / 3

= [$7.1675 + 0 - $8.0825] / 3

= -0.915 / 3

= -0.305

Therefore, Covariance of the stock holding period return with stocks ending price is -0.305