“1. Derivatives pricing models use the risk-free rate to discount future cash flows because these models: A. are based on portfolios with certain payoffs” (CORRECT)
“B. assume that derivatives investors are risk-neutral.”
This answer is incorrect because these models do not assume investors are risk neutral. Most models assume that investors are risk averse.
“C. assume that risk can be eliminated by diversification.”
This answer is incorrect because although nonsystematic risk can (theoretically) be eliminated by diversification, systematic risk cannot be eliminated by diversification. So all portfolios will have some amount of systematic risk. It follows that a fair return on a fully diversified portfolio should be above the risk-free rate of return, by virtue of the fact that the portfolio is not entirely risk-free.
“2. The price of a forward or futures contract: A. is typically zero at initiation.”
One should exercise care when using the terminology of futures and forwards. In this context, the “price” refers to the futures price, i.e., the price paid for the underlying asset when the contract matures. If you agree to pay $100 for a share of stock one year from now, then the share of stock is the underlying asset and the futures price is $100. The error someone might make is to conflate the idea of futures price with value of the futures contract. They are not the same thing.
Answer A is wrong since the value of a futures contract, meaning the present value of the futures price, minus the current spot price, must be zero at initiation. However, the futures price would not be zero at initiation of the contract.
“B. is equal to the spot price at expiration.”
Answer B is incorrect since once the futures price is agreed to at initiation of the contract, it does not change. However, the value of the futures contract will certainly change throughout the life of the futures contract, since the value of the underlying will change. The value of the futures contract should be zero at contract initiation.
“C. remains the same over the term of the contract” (CORRECT)
“3. For a forward contract on an asset that has no costs or benefits from holding it to have zero value at initiation, the arbitrage-free forward price must equal: A. the expected future spot price. B. the future value of the current spot price. C. the present value of the expected future spot price.”
The spot price can be thought of as a random variable. If you were able to predict the mean of the spot price in the future, without reference to the risk free rate, the expected value of the spot price in the future would simply be the same as the spot price now. Thus choice A is incorrect. The present value of that expected future spot price would be something less than the current spot price because the term “present value” implies you are discounting at the risk-free rate back to the present. Thus choice C would be incorrect.
If the no-arbitrage condition holds, (which in theory it does, in practice it might) the relationship between the current spot price and the forward price must take into account the risk free rate: _forward price = (spot price)(_1 + r)^T.
I hope this is helpful to you.