Question

#1. The spot price of a certain asset is S0 = $50400 And the price for a six months maturity future over such underlying asset is F= $53550

a) Compute the risk free rate (continuous compounding).

b) Combine the spot and the future markets so as to replicate debt. Your wealth is $ 50,400,000, show two strategies that: b1) Invest purchasing both, the underlying asset and bonds. b2) Invest purchasing only the underlying asset and borrowing money.

Answer 1

Ans a) Future value = spot value * e^(r*t)

53550 = 50400 * e^(r*.5)

e^(.5r) = 1.0625

.5r * loge = log(1.0625)

.5r = .060625

r = 12.13%

Ans b) One will invest half of wealth in the assets and half of wealth in the liabilities. Thus the correct answer is $25200 in asset and $25200 in bond.

So here investor will borrow $50400 and invest in asset and during maturity will pay back the money of $53550 by selling the asset if the price of asset will be more than $53550 then he will earn a profit else make loss.