The nonsense of VaR

Value at Risk - Just a few short years ago it was all the rage. The question on the trading floor was not 'how big is your position', but 'What's your VaR?'. Over the past couple of years, VaR has taken a battering from many who have pointed out that VaR is all very well for dealing with day-to-day volatility, it is truly useless for understanding worst-case scenarios because it is reported to a confidence level, usually 95 or 99%, and thus deliberately excludes the 'fat tail' or abnormal deviations that are the really important and interesting part of risk management. Being told that your portfolio has a daily VaR of $10 million, with 99% confidence is all very well, but what does it actually mean, in real terms? Risk management shouldn't primarily be about fluctuations in value (i.e. volatility), but about permanent impairment of wealth - i.e. rare, cataclysmic events that wreck portfolios terminally, not the daily back-and-forth. VaR is just another volatility-based definition of 'risk' - relevant perhaps, but not the kind of risk that a portfolio manager or trader should focus on. However, I want to focus on another serious flaw in the VaR measurement, one that has been overlooked. This is that it measures volatility using past data as its input. More specifically, through there are differences in calculation, VaR typically uses the past x days of a market as typical of the volatility in that market, and uses this figure to derive its confidence levels. This in turn means that VaR is always behind the curve as market volatility changes. Think this is a theoretical argument? Well, allow me to make it a very real one. Using figures culled from Bear Stearns annual reports over the past decade, we can see what this really means. Over the nine and a half years between Q1 1998 and the end of Q2 2007, Bear's traders experienced just 5 days of loses above the 95% daily VaR limit. In Q3 2007, however, BSC succumbed to 10 such days. In Q4 they had 16, and in Q1 2008 (just before BSC went the way of the dodo), they experienced a further 8. That's 34 days where the day's trading loss exceeded the firm's 95% confidence level in a mere 9 months. Assuming a 21 trading day month, that implies that loses exceeded the VaR limit 18% of the time in a 9 month period. Equally worryingly, it came after just 5 such days in nearly the entire previous decade. Figures from Goldman Sachs, Morgan Stanley and Lehman Brothers show similar rapid increases in the number of days where VaR limits were exceeded. The problem then is that not only does VaR fail to account for the really crucial 'fat tail' risk, but, as conventionally configured, it isn't even that good at quantifying volatility due to an over-reliance on the near past. Bad, VeRy bad!

The bonus system and the financial crisis

An awful lot has been written about the link between "banker's bonuses" and the credit crunch in the past two years. In fact, I'd wager that every major newspaper, magazine, and other periodical in the Britain and America, whether finance-related or not, has had at least one article on the subject recently. The jist of these articles runs along the lines of: the financial crisis was caused, in whole or (significant) part, by bankers, from the CEO down, being incentivised by the bonus structure to run very large risks with their shareholder's capital. They did this because the ordinary bonus system is a particularly bad example of what can be called the 'trader's option'. The 'option' metaphor arises because bonus payments offer unlimited potential payoffs (dependent only on how much money you make - motivating you to take more risk) pitted against limited potential downside (if you lose enough money, you'll be fired, but will be able to keep the bonuses paid in prior years). These articles draw an explicit link between what is seen by many people as a wholly unfair and unjust system of pay with the financial crisis which has caused a global recession. This is, however, a vast oversimplification that doesn't stand up well to the facts.

Please don't misunderstand me. Firstly, it is very true that the bonus system is wrongly set up - it does offer people payoffs for taking lots of risk, especially 'blow up' risk. Secondly, that banks were assuming too much risk is indisputable, but it wasn't as a result of the bonus system. Why do I say this. Look no further than two poster children for the irresponsibility that brought about the crisis: Dick Fuld of Lehman Bros. and Jimmy Cayne of Bear Stearns.

According to Forbes, in March 2007, James B. Cayne was worth $1.3 billion. Richard S. Fuld Jr. was worth $1 billion. Of Cayne's wealth, the vast majority (about $1bn) was invested in Bear Stearns (BSC) stock, which had peaked in Jan. '07 at just over $171/share. When Cayne sold his more than 5.6 million shares in March 2008, he received just $61.3m for them - about $10.84/share (though he had sold several hundred thousand shares over the previous year). That represents a loss of about 94%, or roughly $900 million. Estimates of the amount Fuld lost vary widely, with New York Magazine reporting he owned 10 million shares when Lehman filed on 15th Sept 2008, and lost almost all the $1 billion. Other sources say he only held about 3-4m shares when LEH filed for bankruptcy, and lost about $250m. By Fuld's own estimate in his Congressional testimony, however, he took about $350m out of the firm over the 14 years he ran it. Whatever the truth, Dick Fuld certainly lost several hundred million dollars from Lehman's failure. Certainly no one can say Dick Fuld and Jimmy Cayne weren't well incentivised to do the best they could for shareholders of LEH and BSC - Cayne owned about 5% of the company and both men had most of their net worth tied up in the stock. Also, note that these are shares, not options or other derivatives. Additionally, both men knew their banks and the industry inside out, as they had both worked for their respective firms for almost 40 years (both started in 1969, as it happens). Cayne, having been Bear's President since 1985, had been appointed CEO in 1993, the same year Fuld became CEO of LEH. Well, the bonus-theorists contend, maybe others in the company were running risks the CEO's weren't aware of. Well... nice idea, but I'm afraid not. Cayne in particular was very encouraging of his firm's leading position in the mortgage-backed securities (MBS) market. He boasted of BSC's prowess in mortgage origination/securitisation at every opportunity in the 2006 annual report (I'd love to know if the 2007 AR was the same but unfortunately I don't have it). LEH bought Aurora Loan Services and BNC Mortgage to allow them easier, cheaper access to mortgages to securitise. Well, maybe the problem with bonuses was further down the pipeline - maybe it's the bankers and traders on the floor who were running obscene risks for short-term gains. Well, possibly, but I'm afraid this argument doesn't really hold water - you see, according to CNN, BSC was more than 30% owned by its employees, as was Lehman Brothers (according to the company). So both firms' 'big beasts' (who owned much of this employee shareholding due to their compensation plans) had a whole lot of incentive not to screw up, yet screw up they did, and badly. Reform the bonus system if you want (and it does need reforming), but don't pretend it had anything to do with the crisis. If it were up to me, I'd simply hold a percentage of each annual bonus in an escrow account (or shares that couldn't be sold) for 5 (or ideally 10) years, and use a 'malus' or clawback system like UBS or Goldman, whereby future losses are offset against previous bonuses. This would take the majority of the venom out of the 'trader's option'.

The Yale model and why its still one of the best portfolio construction methods out there

My first post will deal with some articles written by Aaron Pressman at BusinessWeek, criticising the 'magic formula' (as he calls it) of asset allocation described in David Swenson's book Unconventional Success (US). In the first ("Yale investing guru Swensen missed problems with his advice"), Pressman criticises the US model for poor performance during the financial crisis. While I don't disagree with his point that the portfolio described in US is very different from the Yale model, this is unavoidable due to two points:

1) The average investor simply can't invest in most high-quality alternative asset classes, as Yale does, due to SEC rules and the lack of a retail segment in these markets. Swensen's 'magic formula' as Mr.Pressman calls it ('suggestion' would be more accurate), is an approximation to allow for this (though I believe that Yale's reliance on alternative assets is much less important than the role of hard/'real' assets, as a driver of outsized returns).

2) Recognising that the 'average investor' will neccessarily have no special knowledge about the market, the US portfolio is entirely Beta-driven. This means it will, by defintion, have a different setup to a large institutionally portfolio managed full-time by one of the most famous and influential investment managers in the world, who, presumably, has quite an information edge, due to the budget, research staff, and other sources of information he can command.

Furthermore, I feel that Mr. Pressman has neglected to consider several major points in his article:

(a) He states that the US allocation (which lost 32% in the 12 months to March 2008) could be improved upon by "... a simple mix of say 70% U.S. stocks and 30% bonds, which lost only 25%. A 60/40 mix dropped 19%.", but he doesn't give any indication that he understands why this occurred. When you understand why it occurred, the reason for these varying performances becomes obvious. The reason that the 60/40 portfolio does best is because, in mid 2008, the markets rapidly went from predicting an inflationary to a deflationary scenario. Inflation-hedging 'hard' or 'real' assets (commodities, real estate, TIPS) looked hugely overpriced, and Treasury bonds went through the roof. The US portfolio is heavily weighted in hard assets (though not commodities), as an inflation hedge. What Mr. Pressman is saying essentially boils down to, the fact that, in deflationary times, bonds do super-duper, and stocks and hard assets do very poorly! This is not news, and leads on to my second point.

(b) Viewing the portfolio returns over timeframes of less than 10 years leads to misleading conclusions. In his second article ("Revisiting the debate over Yale's investing guru, David Swensen"), Mr.Pressman says,

If you invested $10,000 in the magic formula at the beginning of 2005, when the book came out, how much would you have 4-1/2 years later on May 31, 2009 with annual rebalancing? $10,275. That's worse than if you'd kept the whole sum in T-bills or a money market fund and virtually identical to the $10,268 you'd have investing a BENCHMARK EXAMPLE of 70% U.S. Stocks and 30% U.S. Treasuries.

and from this draws the frankly hilarious conclusion that, "Running the results of the six-fund magic formula over longer periods doesn't help Swensen's case much." Well, 4 or 5 years is possibly medium-term, and definitely not long term. Run the portfolio over, say, 1966-1982, and see what happens to the benchmark example. In all seriousness, run the portfolio over at least 10 and preferably 20-40 years, and if you still get the same results, I might take it seriously. Of course, you won't get the same results, beacause what Yale and other endowments and institutions wisely learned from the 1970's was that it was disastrous not to have any inflation-hedges in a long-term portfolio. Most astute investors will be aware that bonds and stocks both act poorly in the face of inflation. The 1970's were just such a time. Rather worryingly, Mr. Pressman, states, "We’ve also just experienced a 30-year or so trend of declining long-term interest rates and inflation in the U.S. that gave a nice tailwind to certain assets. An asset mix constructed based on returns and volatility during that period might not work so well if the next 30 years see a very different interest rate backdrop.", implying, I think, that he believes an inflationary environment would make Swenson's portfolio even further underperform the 70/30 benchmark. As I hope I have made clear above, this statement simply doens't make any sense after a rational analysis of the US portfolio structure.

(c) Mr. Pressman states,

Finally, commenter 'Finn' [that's me!] makes reference to modern portfolio theory, the efficient frontier and the benefits of diversification. These are excellent theories but they're constructed on top of numerous simplifying assumptions about how the world works. I'd suggest taking a look at some of the more recent research about how MPT has failed of late.

Now, I'm not exactly the biggest fan of investment theory, and I wholeheartedly agree with Mr. Pressman that MPT should not be actually used for building portfolios (i.e. don't start plugging numbers in and taking the results as gospel). As a guide to thinking about portfolio construction, however, I find it helpful. It shows you an idealised conception of how the world should work (but doesn't!). That is why I mentoned MPT, as the theoretical underpinning of Mr. Swenson's model - diversification makes sense under conditions of ignorance (hence, the all-Beta portfolio). Using, for example Jeremy Siegel's Stocks for the Long Run, and the ABN Amro Global Investment Returns Yearbook data for stocks, bonds, cash, gold etc, we can see that, over very long periods, asset classes do have certain characteristics - cash (essentially a very short-term bond) yields, essentially, inflation-rate returns, as does gold (though with much more volatility). Long-term bonds do very poorly in times of inflation, and very well in times of deflation. Stocks are an excellent hedge for inflation over the long run, but actually (and, it looks like, irrationally) a very poor inflation hedge over the short term. This is how I use MPT - as a framework through which to think about these various correlations.

(d) Finally, Mr. Pressman makes the mistake of quoting NN Taleb to this Taleb fan, evidently unaware that (i) Taleb suggest putting 90% of your portfolio in T-bills and the balance in venture capital or options, (ii) more importantly, Taleb would absolutely abhore drawing firm conclusions about anything, including expected long-run portfolio performance, from inadequate past data (see 'Fooled by Randomness', 2nd ed. pp. 64-69, about the difference between noise and information), as Mr. Pressman does when he talks about performance over the past 1-5 years, as described above in (b).

In sum, Mr. Pressman be be right that the portfolio suggested in US did not do well over 2008-2009, but his analysis proves nothing about the long-term viability of the portfolio. Since it is the long-term performance we should care about, this to me suggests that these articles do not contribute very much.