Risk-free return

The textbook says that if at time “0” we get “a position in underlying + opposite position in the derivative,” at time “T” we will get "Underlying payoff - Derivative payoff, which is equal to Risk-free return.

If I am holding (long position) a stock and short position on the derivative, technically speaking, the gain/loss on the underlying asset will be offset by the loss/gain on the derivative. My question is, if there is an offset, how comes that the investor can earn risk-free return? As far as I understood the concept, a position in underlying + opposite position in the derivative wil help to avoid the loss, but not gaining, hence, I am confused, where the risk-free return obtained from.

I appreciate if someone can explain me my mistake.


Because your short position on the derivative will not be at the same price as the stock which you have a long position in. The derivative will be priced so that you can earn risk-free return. Otherwise, there will be an arbitrage opportunity.

OK this concept you need to master as it’s al lover the all 3 levels.

You own the stock

You sell the stock and Invest proceeds in Risk free assets (you sold short collected the monies and you are better of by the uncle Sam’s interest :slight_smile:

Underlying payoff - Derivative payoff, which is equal to Risk-free return.

or for Dummies:

CAPM= Rf + beta*market risk premium - if you removed risk component you are left with Rf rate out of the CAPM formula

Hope this helps

I understood these concepts, but my confusion is about the following:

Let us say I have bought (own) a stock and sell the derivative on that stock. Theory says that by doing so, I will be earning risk-free return. In my understanding, however, if the price of the stock goes up by $3 it means that the value of derivative will go down by $3 as well. Conversely, if the stock goes down and I am incurring $3 loss, it will be offset by the $3 gain on the short position of the derivative. For me, the only thing that makes sense is that by having that compensation I have a 0 return but not risk free return as I am getting nothing.

Hope, someone will explain what is wrong in my assumption

Look at the definition of short sales. You borrow asset form somebody and you sale that asset => collect monies and invest in Tbills . You need go beyond simple hedging here. Look at long, short and Rf return.

This is also very popular concept in CFAI. Master it!

buy TSLA for 300, but since E.M loosing his credibility you afraid that stock goes to 200. So you sell short forward on TSLA for F0=303

if you correct you lost 100 on long and gain 100 on short forward and earn risk free rate of 1% no matter what


this explanation was awesome.