A Risk Measure for S-Shaped Assets and Prediction of Investment Performance

In this paper, we study the option valuation of S-shaped assets. S-shaped assets are frequently encountered in technological developments, grant funding of research projects, and to a degree, hedge funds and stop-loss controlled trend-following investment vehicles. We conclude that the quantity σ2/μ (variance of return/expected return) replaced the traditional variance risk measure σ2 in the Black-Scholes option valuation formula. We further study the interesting property of σ2/μ in predicting the turning point of performance of a portfolio of hedge funds in the early months of 2008 (and indeed, for earlier historical turning points).