Jeffery and Smith (Equity Release Mortgages: Irish & UK Experience, p.30) discuss the apparent paradox that when we use a ‘real world’ model to project a forward price, then calculate the expected value of put and call options at different strikes, the internal rate of return of those options is considerably different from that obtained using the Black formula. See their table which I have copied below. Put options even have negative discount rates.
Taking the case of the put options, how can we rationalise these negative discount rates? Why would an investor even consider an asset that is expected to lose money, let alone one as risky as a put option which has a chance of expiring worthless, losing everything?
They continue.
The answer is that few rational investors hold a portfolio 100% in a put option. Rather, a put option is a form of insurance held in connection with other assets. An investor in shares can, sometimes with a modest outlay, acquire a put option that substantially mitigates losses in a market crash. The willingness to accept a negative expected return on the put option reflects the reduction of risk to the portfolio as a whole. This is the same reason that buyers of household or motor insurance would not expect (or hope) to make a profit on that insurance.
Are they right? Does the ‘willingness to accept a negative expected return’ really reflect the need to reduce the risk?
Continue reading “The forward paradox”
