The Price of Risk: From Modern Portfolio Theory to Leveraged Portfolio Theory

Abstract

The Modern Portfolio Theory (MPT) has been the cornerstone of the asset allocation for over 40 years. In the past decade though, it led in a rather systematic way to bad investments decisions. One of MPT’s main assumptions, investor risk aversion that translates into volatility aversion, biases financial markets toward low volatility / high extreme risk patterns, such as the recent sub-prime crisis. The proposed Leveraged Portfolio Theory (LPT) removes the most fundamental axiom of the MPT: the hypothesis that risk aversion is an exogenous pattern of investors. Instead in our model risk aversion becomes an endogenous variable, resulting from the supply/demand equilibrium in credit markets. The resulting model leads to the LP function, a trade-off between expected return conditional on blue sky scenarios vs the distribution of worst cases scenarios. Under homogenous expectation hypothesis, market equilibrium is reached when asset’s expected blue sky return is proportional to its extreme beta in respect to the market, i.e. its contribution to market extreme risk. By imposing normal distribution for assets return, we obtain the classical CAPM beta in LPT framework. We show that extreme risk underestimation by lenders typically leads to bubble and bubble burst cycles. Back tests of the model on the past decade show that LPT based risk-budgeting strategy significantly outperforms CAPM strategy type, implying that extreme risk is mispriced by the market.