The Black-Litterman model

The Black Litterman model was developed in 1990 at Goldman Sachs by Fischer Black and Robert Litterman and deals with two problems in classic portfolio optimization:

  1. First, a standard optimization model requires as inputs the expected returns for all assets and currencies. Thus investors must augment their views with a set of auxiliary assumptions, and the historical returns they often use for this purpose provide poor guides to future returns.
  2. Second, the optimal portfolio asset weights and currency positions of standard asset allocation models are extremely sensitive to the return assumptions used.

This article describes an approach that provides an intuitive solution to the two problems that have plagued quantitative asset allocation models. The key is combining two established tenets of modern portfolio theory-the mean-variance optimization framework of Markowitz and the capital asset pricing model (CAPM).

“Global Portfolio Optimization” by Fischer Black and Robert Litterman, Financial Analysts Journal, September 1992.

Link here

Investor bias on favoring high beta stocks, and how take advantage of it

“Betting against beta”, by Andrea Frazzini , Lasse Heje Pedersen, AQR Capital Management, April 2013

“We present a model with leverage and margin constraints that vary across investors and time. We find evidence consistent with each of the model’s five central predictions: (1) Because constrained investors bid up high-beta assets, high beta is associated with low alpha, as we find empirically for US equities, 20 international equity markets, Treasury bonds, corporate bonds, and futures. (2) A betting against beta (BAB) factor, which is long leveraged low-beta assets and short high-beta assets, produces significant positive riskadjusted returns. (3) When funding constraints tighten, the return of the BAB factor is low. (4) Increased funding liquidity risk compresses betas toward one. (5) More constrained investors hold riskier assets.”

Link here

Finiteness of variance and its limitations in quantitative finance

For our 4/26 discussion, a paper by Nassim Taleb, with his typical choleric flair:

“Outside the Platonic world of financial models, assuming the underlying distribution is a scalable “power law”, we are unable to find a consequential difference between finite and infinite variance models –a central distinction emphasized in the econophysics literature and the financial economics tradition. While distributions with power law tail exponents α>2 are held to be amenable to Gaussian tools, owing to their “finite variance”, we fail to understand the difference in the application with other power laws (1<α<2) held to belong to the Pareto-Lévy-Mandelbrot stable regime. The problem invalidates derivatives theory (dynamic hedging arguments) and portfolio construction based on mean-variance. This paper discusses methods to deal with the implications of the point in a real world setting.”

Link to paper

Comparing realized and absolute return volatility measures

This paper compares two different ways to measure volatility, with a survey of techniques that analyze their respective probability distribution, mean-reversion, cross-correlation, and long-term memory effects.

Excerpt: “…two nonparametric measurements have emerged and received wide use over the past decade: realized volatility and absolute return volatility. The former is strongly favored in the financial sector and the latter by econophysicists. We examine the memory and clustering features of these two methods and find that both enable strong predictions. We compare the two in detail and find that although realized volatility has a better short-term effect that allows predictions of near-future market behavior, absolute return volatility is easier to calculate and, as a risk indicator, has approximately the same sensitivity as realized volatility.”

Link to paper

An analysis of Warren’s Buffet’s investment strategy

Buffett’s Alpha. by Andrea Frazzini, David Kabiller, and Lasse Heje Pedersen

The authors find that Buffet has been picking low volatility, low beta stocks with consistent earnings, and then levering up his investment using his insurance float.

“Buffett’s returns appear to be neither luck nor magic, but, rather, reward for the use of leverage combined with a focus on cheap, safe, quality stocks. Decomposing Berkshires’ portfolio into ownership in publicly traded stocks versus wholly-owned private companies, we find that the former performs the best, suggesting that Buffett’s returns are more due to stock selection than to his effect on management.”

Link to paper   Slide version