I-CAPM was first introduced in 1973 by Merton. It is an extension of CAPM which recognizes not only the familiar time-independent CAPM beta relationship, but also additional factors that change over time (hence “intertemporal”).

We have devoted a lot of blog space in the past examining the pros and cons of the Capital Asset Pricing Model (CAPM). The model predicts the amount of excess return (return above the risk-free rate) of an arbitrary portfolio that can be ascribed to a relationship (called beta[1]) to the excess returns on the underlying market portfolio.

Having previously discussed them, let’s compare them. How does the Arbitrage Pricing Theory (APT) stack up against the Capital Asset Pricing Model (CAPM)?

Our quest continues to find out whether hedge fund alpha really exists or is just hype. Recall from last time our documentation of the Capital Market Line (CML). The CML represents a portfolio containing some mixture of the Market Portfolio (MP) and the risk-free rate. It is aspecial version of the Capital Asset Line, ranging from the risk-free rate tangentially to the Efficient Frontier at the Market Portfolio, and then extending upwards beyond the tangent point. Modern Portfolio Theory (MPT) posits that any point on the CML has superior risk/return attributes over any point on the Efficient Frontier. Let’s ponder that for a second – just adding some T-Bills to, say, S&P 500 baskets (our proxy for the Market Portfolio) will improve the risk/return characteristics of your portfolio.

If your entire portfolio consisted only of the cash-purchased Market Portfolio (i.e. the tangent point on the Efficient Frontier), your leverage ratio would be 1 – you are unleveraged. The points on the CML below the Market Portfolio represent deleveraging: adding cash to your portfolio. You are lowering risk and expected return when you deleverage. If you borrowed and sold TBills, and used the proceeds to buy additional Market Portfolio, your new portfolio would be leveraged, and would be a point on the CML above the tangent. Leveraging increases your risk and expected return. If you disregard the effects of borrowing (or margin) costs, then all points on the CML share the maximum Sharpe Ratio, a popular formula for expressing risk/return. Continue reading “Modern Portfolio Theory – Part Three” »

We continue our journey into the wonderland of alpha, taking up with leverage and the Efficient Frontier. We documented last time that a mix of a risky portfolio and the risk-free rate (Rf) yields a linear Capital Asset Line (CAL) within risk-return space. When the mix is varied to decrease the amount of Rf, the riskiness and expected return of the portfolio increase. The mirror image occurs as we increase the relative percentage of Rf in the portfolio mix. We can even borrow at the risk-free rate to purchase additional risky assets for our portfolio – one form of a practice known as leverage. Continue reading “Modern Portfolio Theory – Part Two” »

Hedge funds use an array of strategies to guide trading. Most of these strategies seek to decouple returns from those of the overall market, as measured by a statistic called “beta” (β). Beta is calculated by dividing the covariance of an investment’s return by the variance of a portfolio or market return:

β_{i} = Cov (r_{i}, r_{m}) / Var(r_{m}) where i = an investment, m = market portfolio, and r = return