Quiz-1 (Forward pricing)

First of all, sorry to all of you, for the delayed new posting! But I will try to post them regularly.

Which of the following options is most accurate for measuring the forward price of a commodity or an investment asset, assuming that the investment value of the asset grows continuously at risk-free rate of interest?
a.      S₀ x e^rt
b.      S₀ + e^rt
c.       S₀ / e^rt
d.      S₀ - e^rt

Assuming that that the value of investment asset grows at discrete rate of interest, which of the following formulae correctly explain relationship between the current spot price and forward price of an asset?
a.      S₀ (1+r)^t
b.      S₀ +(1+r)^t
c.       S₀ - (1+r)^t
d.      S₀ /(1+r)^t

A trader invested $520 in an investment asset, with an intention to sell it after 6 months. If the risk-free rate of interest is 4.5% per annum and the value of the asset grows continuously, the forward price of the asset is equal to:

a.      530.70
b.      531.83
c.       531.95
d.      532.05

A trader invested $520 in an investment asset, with an intention to sell it after 6 months. If the risk-free rate of interest is 4.5% per annum and the value of the asset grows on discrete basis, the forward price of the asset is equal to:

a.      530.70
b.      531.83
c.       531.95
d.      532.05

Assume that current spot price of an investment asset is $60 and risk-free rate of interest is 4.0% per annum. The forward price of an investment asset, growing at risk-free rate of interest (continuously) is calculated at time- T_{0 ,}  by the following theoretical forward price formula:

F₀ = S₀ x e^rt

When the traders identify that the above formula does not hold good, they attempt for arbitrage opportunities. If the market quoted forward price does not match the theoretical forward price, then there exists an arbitrage opportunity.

Which of the following statements about the arbitrage opportunities is correct, when the market determined forward price is higher than the theoretical forward price for a maturity period of 6 months?

Answer:

a. Borrow at risk-free rate, buy asset, sell forward

b. Lend at risk-free rate, buy asset, sell forward

c. Borrow at risk-free rate, sell asset and buy forward

d. Lend at risk-free rate, sell asset and buy forward