Question

# Suppose the value of the S&P 500 Stock Index is currently \$1,750. If the one-year T-bill...

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

Question a):

Future Price of the S&P 500 = Sp * e (rf - q) * t

Sp = 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 = Sp * e (rf - q) * t

Sp = 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

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