tag:blogger.com,1999:blog-7905515.post273130819056538065..comments2024-03-14T11:09:32.759-05:00Comments on Falkenblog: Aaron Brown Reviews Finding AlphaEric Falkensteinhttp://www.blogger.com/profile/07243687157322033496noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-7905515.post-62040450072801230362009-07-29T08:59:34.932-05:002009-07-29T08:59:34.932-05:00Aaron: I think the Siegel's finding that volat...Aaron: I think the Siegel's finding that volatility decreases by time horizon is interesting, and a recent paper by Pastor and Stambaugh suggests this is crucially dependent on the fact that this is a sample estimate. If one assumes the mean return has a prior distribution, stocks are actually more volatile over long horizons. See <a href="http://www.nber.org/~confer/2009/SI2009/AP/Pastor_Stambaugh.pdf" rel="nofollow">Are Stocks Really Less volatile in the Long Run?</a>. <br /><br />I think if the CAPM were true, it would not be obvious that low beta investing is better. Given the CAPM is not true, it is. This 'arbitrage' is small, not hedge-fund worthy, but rather, like index investing, a good idea for most investors. Basically, quit chasing last year's big winners, accept a moderate return, and you can get a 1% return premium with lower intuitive measures of risk (beta, volatility). I think an institution like AQR would be in a position to provide this, because it needs to be sold, just as early index funds did. That is, it's obvious based on the math, but counterintuitive to many investors. You need data, theory, and a brand, to really sell this.Eric Falkensteinhttps://www.blogger.com/profile/07243687157322033496noreply@blogger.comtag:blogger.com,1999:blog-7905515.post-1719620105979959352009-07-29T08:47:17.409-05:002009-07-29T08:47:17.409-05:00You get no argument from me, or anyone with a brai...You get no argument from me, or anyone with a brain who has looked at the data, that the lack of relation between sample averages and risk groupings means the simple model cannot be right. I prefer to speak in terms of strategies (e.g. "Buying a diversified portfolio of stocks with measured Betas over 1.5 over the prior three years and shorting a matched diversified portfolio of stocks with measured Betas under 0.75 does not produce consistently positive returns over long periods") because they are precise and testable, with plenty of data. I understand it's simpler to speak of assets, e.g. "high Beta stocks do not have carry a risk premium over low Beta stocks," but there are never enough data to form a conclusion about any individual asset, or even large portfolio of assets. It's even problematic to prove that the S&P500 outperforms T-bills on average. But that's okay because it's strategies that matter, not assets.<br /><br />Now I understand what you meant by that sentence, but I think you're jumping over some basic issues. If you think about one period, then Sharpe ratio (mean excess return / standard deviation) or something else in the same units of dollars / dollars is the natural way to rank portfolios. At the other extreme, if you think about a long sequence of investments, then Kelly (mean excess return / variance) or something else in the units $ / $^2 is natural.<br /><br />This is the difference between portfolio management and risk management. A portfolio manager wants to know the beneficial investor's time horizon, but the size of the investment is a relatively minor consideration. Sharpe ratio declines with time horizon but is independent of size. The risk manager wants to know the size, but time horizon is not important. Kelly increases with bet size, but is independent of time horizon.<br /><br />Therefore, using the diversification argument as you do carries a lot of baggage with it. From a Kelly perspective, the risk of the sum of two uncorrelated gambles is equal to the sum of the risks.<br /><br />In your terms, once someone has found alpha they might choose to run out and raise a lot of money from others to make a one-time killing, and then worry about tomorrow; or they might choose to raise the minimum necessary capital in order to keep as much equity as possible, and grow it exponentially. The first makes sense if you think of standard deviation as risk, if you're a portfolio manager at heart, if you work for a big institution. The second makes sense if you think of variance as risk, if you're a risk manager at heart, if you work for yourself. The first guy loves diversification, both lots of bets and long time horizon, and the CAPM speaks to him. If the CAPM is wrong, he needs a replacement in the same units. The second gal has no use for diversification or the CAPM, however reformulated. She doesn't have a problem that can be profitably analyzed in a single-period model, or even a multi-period extension of a single-period model. She speaks a different language.<br /><br />After reading your book, I think your biggest issue with CAPM would still apply if it were true. In order to write the equation down you have to make assumptions that are incompatible with alpha. I don't mean assumptions that require alpha = 0, I mean assumptions that make the concept of alpha impossible. You don't want a replacement CAPM, you want to work in another dimension.Aaron Brownnoreply@blogger.comtag:blogger.com,1999:blog-7905515.post-25421641616094084592009-07-28T19:59:15.676-05:002009-07-28T19:59:15.676-05:00Right again! I mean volatility. The basic point ...Right again! I mean volatility. The basic point is that diversification lowers risk, and this leads to idiosyncratic risk going to zero, leaving only covariance as the determinate of portfolio volatility. This is the essence of the Markowitz's point, and the surprising thing was that this is not zero (surprising to the conventional wisdom back then). But you are correct, I regret the error.<br /><br />As to expected returns changing over time, this is possible, but with junk bonds vs. inv. grad bonds, high beta stocks vs. low beta stocks, out-of-the-money calls vs. in the money, the changes in their expected returns due to stochastic discount factors, and changes in their 'betas' (to the SDF of choice), are insufficient to explain the fact that the sample averages over all the time we have show no relation, if not a negative relation, between groupings of low and high risk. For example, a beta 2.0 stock will change its beta over time, usually towards 1, but on average the betas are well above 1, and the risk premiums should be above those stocks with betas around 0.5 (whose betas may move up to 0.7). Over long periods of time, assets with higher volatility, default risk, uncertainty, and covariance of the market have at best equaled the return of their asset class counterparts. I don't think 'expected returns' can save them. I think going forward, avoiding these assets, for someone looking to invest in size, is I think optimal. That is, if you just want to maximize your Sharpe or Information Ratio, it seems a very good strategy.Eric Falkensteinhttps://www.blogger.com/profile/07243687157322033496noreply@blogger.comtag:blogger.com,1999:blog-7905515.post-15226336920994614222009-07-28T19:00:54.231-05:002009-07-28T19:00:54.231-05:00Thanks for a graceful response to a mixed review.
...Thanks for a graceful response to a mixed review.<br /><br />I am puzzled by one point, you say that the sum of the variances of two random variables is less than the sum of their variances. But that is only true for assets with negative covariance. The formula is:<br /><br />Variance(A + B) = Variance(A) + Variance(B) + 2*Covariance(A,B)<br /><br />I would not have singled out the omission of "sum of" by itself, but in this case it left me guessing about your meaning. I'm still guessing.<br /><br />I disagre with, "expected returns should equal average returns over large enough sample, just as a sample mean converges to the population mean over time." The trouble is parameters are not constant over a sufficiently long period to make this true in practice. Expected return of individual assets has to be a matter of faith, not statistical proof. That doesn't mean you can't get reliable empirical results about strategies.<br /><br />I agree wholeheartedly that the deviation of ex post asset returns from simple theory means the simple theory is wrong. There is plenty of evidence for that. But I think you and I are both really interested in future returns, not past data or anyone's expectations. If you expressed your theory in terms of the best possible current prediction of future returns it would retain all its practical value, and would fit in quite well with modern academic theories.<br /><br />The past is for archeologists. A dead record of historical prices is problematic to analyze, because you don't really know what you could have executed at what price. And even if you explain it correctly, you have only explained how things used to be. Finance is much to dynamic for that to have much value.<br /><br />I love your book because it deals with living issues in useful and important ways, but I still consider it an ugly description of the dead past.<br /><br />I concede Taleb is an acquired taste, although I found much more in his books than you did. I did not cite him as someone so authoritative you had to mention him, but as the most obvious source on the subject.Aaron Brownhttp://www.eraider.comnoreply@blogger.comtag:blogger.com,1999:blog-7905515.post-60725387527379251802009-07-27T10:43:55.743-05:002009-07-27T10:43:55.743-05:00"this book did not benefits from extensive ve..."this book did not benefits from extensive vetting."<br /><br />Nor the blog! :)<br /><br />That's OK though - I'd rather see a good blogger spend more time writing new posts than proof-reading existing blog posts.Michael Stackhttps://www.blogger.com/profile/06879136691984411820noreply@blogger.com