Question

The S&R index spot price is 1100, the risk-free rate is 5%, and the continuous dividend yield on the index is 2%. a. Suppose you observe a 6-month forward price of 1120. What arbitrage would you undertake? b. Suppose you observe a 6-month forward price of 1110. What arbitrage would you undertake?

Answer 1

Answer:

a) Cash-and-carry-arbitrage would be used

b) reverse cash and carry arbitrage would be used

Explanation:

a. Suppose you observe a 6-month forward price of 1120

Given that:

Spot price ($S_0$) = 1100

Time (T) = 6 months = 6/12 years = 0.5 year

Risk free rate (r) = 5% = 0.05

Divided (d) = 2% = 0.02

observed forward price = 1120

The fair forward price ($F_{0,T}$) is given as:

$F_{0,T}=S_0e^{(r-d)T}=1100 * e^{(0.05-0..02)0.5}=1116.62$

Therefore the forward price of 1120 is expensive, creating a long forward of 3.38

b. Suppose you observe a 6-month forward price of 1110. What arbitrage would you undertake

Given that:

Spot price ($S_0$) = 1100

Time (T) = 6 months = 6/12 years = 0.5 year

Risk free rate (r) = 5% = 0.05

Divided (d) = 2% = 0.02

observed forward price = 1110

The fair forward price ($F_{0,T}$) is given as:

$F_{0,T}=S_0e^{(r-d)T}=1100 * e^{(0.05-0..02)0.5}=1116.62$

Therefore the forward price of 1120 is expensive, creating a short forward of 6.62, reverse cash and carry arbitrage would be used