LONDON QUANT GROUP 2010 CHALLENGE
“LELAND’S LOST THEOREM”
At the Annual Investment Seminar held in Cambridge last September, John O’Brien presented a paper on “The Retirement Investing Challenge”. In this paper he pointed out some weaknesses of the currently-fashionable Glide Path, Target Date, Life-Cycle funds being offered to individual investors for retirement saving, and proposed a better way of investing for retirement.
This is the Bond-plus-Call, Target-Date Life Cycle Fund, containing just two assets. The first is aZero-coupon Discount Bond, for downside protection. The amount invested in this Bond is just sufficient to give the investor back their starting capital at maturity (i.e. the Target Date). The remaining amount of the initial capital is used to buy a plain vanilla call option on the equity market (or some other risky asset), for potential gains.
John went on to describe a variant of this, which he called (with an almost English sense of humour) the Perpetual Lock & Roll Strategy. This involves cashing out earlier than the Target Date if the value of the option exceeds some pre-determined ‘gain lock’ amount. The investor then begins again with the increased amount of capital.
During the course of his presentation, John asserted that the Expected return of this Bond-plus-Call Option strategy was the highest of any unlevered, path-independent strategy assuring the same level of downside protection. I had heard him make this assertion once before, and had challenged him to prove it. Unfortunately, at the Cambridge Seminar, he was obliged to announce that when his colleague Hayne Leland had looked for the proof, he had been unable to locate it amongst the many papers in his office.
The London Quant Group therefore issues the following challenge: we will pay a prize of £100, plus a further £100 from myself, for the first person to produce a proof of this theorem, or a counter-example which clearly disproves it. The winner will also reap untold glory from being lauded on our new website (due to be unveiled early in 2010), which should be very helpful in subsequent bonus discussions with their employer.
The Challenge will stand until someone wins the prize. Entries should be sent to Liisa.Young@lqg.org.uk The judging will be done by the London Quant Group’s Management Committee, whose decision in this matter will be final. And obviously correct.
Jason MacQueen, Chairman LQG