Question

Suppose the value of the S&P 500 Stock Index is currently $1,750. If the one-year T-bill rate is 5.3% and the expected dividend yield on the S&P 500 is 4.6%. a. What should the one-year maturity futures price be? (Do not round intermediate calculations.) Futures price $ b. What would the one-year maturity futures price be, if the T-bill rate is less than the dividend yield, for example, 3.6%? (Do not round intermediate calculations.) Futures price

Answer 1

Question a):

Future Price of the S&P 500 = S_p * e ^{(rf - q) * t}

S_p = Current Market Price = $ 1,750

rf = Risk free rate = T-bill rate = 5.3%

q = Dividend yield = 4.6%

t = time to maturity = 1 year

Future Price = $1,750 * e ^{(5.3% - 4.6%) * 1}

= $1,750 * e ^0.007

= $ 1,750 * 1.00702455727

= $ 1,762.293

Question b):

Future Price of the S&P 500 = S_p * e ^{(rf - q) * t}

S_p = Current Market Price = $ 1,750

rf = Risk free rate = T-bill rate = 3.6%

q = Dividend yield = 4.6%

t = time to maturity = 1 year

Future Price = $1,750 * e ^{(3.6% - 4.6%) * 1}

= $1,750 * e -0.01

= $ 1,750 * 0.99004983374

= $ 1,732.587

= $ 1,762.293