Category Archives: Risk

Are markets efficient? Let the two Nobel Economics Laureates debate!

Two Nobel laureates in economics from the University of Chicago, Eugene Fama (2013) and Richard Thaler (2017) debate the efficient market hypothesis. This debate is required viewing for anyone with even a remote interest in finance! (spoiler alert – virtually all derivatives pricing models covered in Finance 4366 assume that the underlying asset follows a random walk, which corresponds to the so-called “weak form” of Fama’s efficient market hypothesis)…

Eugene F. Fama and Richard H. Thaler discuss whether markets are prone to bubbles.


Important empirical evidence on hedge fund performance…

An ongoing debate in finance is whether “active” investment strategies can outperform “passive” strategies. The empirical evidence in favor of passive strategies which appears in studies published by peer-reviewed scientific journals is overwhelming. For example, in studies of mutual fund performance, passive strategies almost always blow away active strategies. Similarly, the empirical evidence on frequency of trading by “retail” customers is that on average, portfolio performance is inversely related to trading frequency; i.e., the more people trade, the worse they do. Even hedge funds chronically underperform passive investment strategies. For example, the authors of a 2011 Journal of Financial Economics (JFE) article entitled “Higher risk, lower returns: What hedge fund investors really earn” find that hedge fund returns are on the magnitude of 3% to 7% lower than corresponding buy-and-hold fund returns, reliably lower than the return on the Standard & Poor’s (S&P) 500 index, and only marginally higher than the riskless rate of interest.

Era of Calm Ends as Volatility Returns to Markets

With the return of volatility in stocks, those investors and trades that profit when markets are calm are suffering heavy losses.
The above referenced WSJ article (published yesterday) tells a very interesting story about volatility as an asset class. VIX exchange-traded products (such as Credit Suisse’s now infamous and soon-to-become-defunct) VelocityShares Daily Inverse VIX Short-Term exchange-traded note (XIV)) were originally conceived of in the aftermath of the global financial crisis as a form of insurance against against increases in market volatility.
As we have previously discussed (see “On the relationship between the S&P 500 and the CBOE Volatility Index (VIX)“), returns on the S&P 500 stock market index and VIX tend to be strongly negatively correlated with each other.  Thus, VIX exchange-traded products such as XIV offer investors the opportunity to hedge against increases in volatility.  Indeed, by reversing the letters in the VIX ticker symbol, the VelocityShares Daily Inverse VIX Short-Term exchange-traded note in particular effectively branded itself as a financial product which hedges volatility.  However, as market volatility subsided during recent months and years, many investors began to sell rather than buy products such as XIV in hopes of boosting portfolio returns.  With stocks trading at historically low volatility levels lately, this strategy seemed to be working pretty well for many investors; that is, until this past week when volatility made its comeback:
The next graph shows the time series for daily closing prices on XIV and on VIX, from 11/30/2010 (which is the first day for which daily data for XIV are available) through yesterday (2/6/2018):
 Within this date range, the correlation between XIV and VIX is -.5608.  Of course, the most interesting aspect of this graph corresponds to the enormous drop in XIV from its all-time closing high of 144.75 (on January 12, 2018) to 7.35 at the close yesterday.  On the same day that XIV reached its all-time closing high,  VIX closed at 10.16, but stood at 37.32 at the close on Monday, February 5.

A Random Walk Down Wall Street

In my opinion, if you were to read only one book about finance, it would have to be “A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing” by Burton G. Malkiel. Malkiel’s book (now in its 11th edition) provides a compelling argument in favor of efficient markets theory and investing in (passively managed) index funds.

Efficient market theory implies that stock prices follow a random walk. These ideas were originally conceived of by Professors Paul Samuelson and Eugene Fama in the 1960’s, and subsequently popularized by folks like Professor Malkiel. In Finance 4366, we rely extensively upon the notion that prices of speculative assets (e.g., stocks, bonds, commodities, foreign exchange, etc.) follow random walks as we consider the technical details associated with pricing and hedging risk using financial derivatives.

The Index Fund featured as one of “50 Things That Made the Modern Economy”

Tim Harford also features the index fund in his “Fifty Things That Made the Modern Economy” radio and podcast series. This 9 minute long podcast lays out the history of the development of the index fund in particular and the evolution of so-called of passive portfolio strategies in general. Much of the content of this podcast is sourced from Vanguard founder Jack Bogle’s September 2011 WSJ article entitled “How the Index Fund Was Born” (available at Here’s the description of this podcast:

“Warren Buffett is the world’s most successful investor. In a letter he wrote to his wife, advising her how to invest after he dies, he offers some clear advice: put almost everything into “a very low-cost S&P 500 index fund”. Index funds passively track the market as a whole by buying a little of everything, rather than trying to beat the market with clever stock picks – the kind of clever stock picks that Warren Buffett himself has been making for more than half a century. Index funds now seem completely natural. But as recently as 1976 they didn’t exist.  And, as Tim Harford explains, they have become very important indeed – and not only to Mrs Buffett.”

Warren Buffett is one of the world’s great investors. His advice? Invest in an index fund

Insurance featured as one of “50 Things That Made the Modern Economy”

From November 2016 through October 2017, Financial Times writer Tim Harford presented an economic history documentary radio and podcast series called 50 Things That Made the Modern Economy. This same information is available in book under the title “Fifty Inventions That Shaped the Modern Economy“. While I recommend listening to the entire series of podcasts (as well as reading the book), I would like to call your attention to Mr. Harford’s episode on the topic of insurance, which I link below. This 9-minute long podcast lays out the history of the development of the various institutions which exist today for the sharing and trading of risk, including markets for financial derivatives as well as for insurance.

“Legally and culturally, there’s a clear distinction between gambling and insurance. Economically, the difference is not so easy to see. Both the gambler and the insurer agree that money will change hands depending on what transpires in some unknowable future. Today the biggest insurance market of all – financial derivatives – blurs the line between insuring and gambling more than ever. Tim Harford tells the story of insurance; an idea as old as gambling but one which is fundamental to the way the modern economy works.”

It Has Been a Near-Perfect Investing Environment. But It May End Soon.

As this article from today’s WSJ points out, the “near-perfect” environment is in reference to a two decade-long financial market anomaly (dating back to the late 1990s) in which stock and bond  have tended to move in opposite directions.  Thus, investors have been able to (quite effectively) hedge risk by owning both asset classes.
For two decades, government bonds have provided what amounts to free insurance against stock-market struggles. But that’s a historical anomaly.

Statistical Independence

During last Thursday’s Finance 4366 class meeting, I introduced the concept of statistical independence. This coming Tuesday, much of our class discussion will focus on the implications of statistical independence for probability distributions such as the binomial and normal distributions which we will rely upon throughout the semester.

Whenever risks are statistically independent of each other, this implies that they are uncorrelated; i.e., random variations in one variable are not meaningfully related to random variations in another. For example, auto accident risks are largely uncorrelated random variables; just because I happen to get into a car accident, this does not make it any more likely that you will suffer a similar fate (that is, unless we happen to run into each other!). Another example of statistical independence is a sequence of coin tosses. Just because a coin toss comes up “heads,” this does not make it any more likely that subsequent coin tosses will also come up “heads.”

Computationally, the joint probability that we both get into car accidents or heads comes up on two consecutive tosses of a coin is equal to the product of the two event probabilities. Suppose your probability of getting into an auto accident during 2017 is 1%, whereas my probability is 2%. Then the likelihood that we both get into auto accidents during 2017 is .01 x .02 = .0002, or .02% (1/50th of 1 percent). Similarly, when tossing a “fair” coin, the probability of observing two “heads” in a row is .5 x .5 = 25%. The probability rule which emerges from these examples can be generalized as follows:

Suppose Xi and Xj are uncorrelated random variables with probabilities pi and pj respectively. Then the joint probability that both Xi and Xj occur is equal to pipj.