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Dr. Alex Castaldo

01/09/05
Four Scholarly Reviews
1. "Variance Risk Premia" by Peter Carr, Liuren Wu; 
2. Cross-Industry Momentum by Lior Menzly, Oguzhan Ozbas;
3. Stock Returns, Aggregate Earnings Surprises, and Behavioral Finance, by Jonathan Lewellen, S.P. Kothari, Jerold B. Warner. 
4. The Cross-Section of Volatility and Expected Returns, by Andrew Ang, Robert Hodrick, Yuhang Xing, Xiaoyan Zhang

Until two years ago I used to attend the American Finance Association meetings during the first weekend of the year (the 2005 meeting is in Philadelphia). Now that the papers presented are easily available on the Web, I can review them in the comfort of my own home. I will summarize four papers that I found interesting.

1. "Variance Risk Premia" by Peter Carr, Liuren. [The well-known Peter Carr is co-author on some papers with Dailyspec's Tony Corso, and Liuren Wu is a former colleague of mine at City U]

Abstract:

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. Ignoring the small approximation error, the difference between the realized variance and this synthetic variance swap rate quantifies the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premia on five stock indexes and 35 individual stocks.

My take:

Bird's eye view of the motivation for this research: Return variances change randomly over time, so investor faces at least two sources of uncertainty, namely the uncertainty about the return as captured by the return variance, and the uncertainty about the return variance itself. We want to know how these two sources of uncertainty affect the prices of securities and portfolios.

I'll skip the details of how the 'variance swap rate' and the 'variance risk premium' are computed and focus on the empirical results. Suffice it to say that when enough options are traded on any asset these two parameters can be estimated from the options prices, the price of the underlying and the historical volatility. Mainly what we are interested in is the 'variance risk premium'.

The data from OptionMetrics LLC starts in January 1996 and February 2003 (OptionMetrics is the best available option database IMHO). Five stock indexes and 35 individual stocks were studied.

The mean variance risk premia are found to be negative for all of the stock indexes and for most of the individual stocks. The largest t-statistics come from the S&P 500 and S&P 100 indexes and the Dow Jones Industrial Average, which are strongly significant. "Therefore, we conclude that investors price heavily the uncertainty in the variance of the S&P and Dow indexes" i.e. are willing to pay a lot to transfer the risk of variance changes to someone else. (They can do this by being long an appropriately designed portfolio of options). "The negative sign of the variance risk premia implies that investors are willing to pay a premium, or receive a return lower than the riskfree rate, to hedge away upward movements in the return variance of the stock indexes. In other words, investors regard market volatility increases as extremely unfavorable shocks to the investment opportunity and demand a heavy premium for bearing such shocks.".

"However, the average variance risk premia on the Nasdaq-100 index and the individual stocks are much smaller. [...] Thus, we conjecture that the market does not price all return variance variation in each single stock, but only prices the variance risk in the stock market portfolio."

After testing the CAPM and FF models the authors conclude that "neither the original capital asset pricing model nor the Fama-French factors can fully account for the negative variance risk premia on the stock indexes. Therefore, either there exist a large inefficiency in the market for index variance or else the majority of the variance risk is generated by an independent risk factor that the market prices heavily". In other words this priced risk factor is above and beyond the risk premium of the CAPM. "We leave the study of economic foundations for the negative variance risk premia for future research."

Mr. E comments: Now I know why Tony and I always disagree!

Tony Corso comments:

there is a reason why my name is not on this paper . . .

it centers around my belief that forward prices [and options on same] of commodities [well,ok, maybe just backwardated commodities] really are opinions/predictions about future spot prices . . . whereas futures prices on stock indexes are pretty much always priced on cash and carry arbitrage, so they say nothing about predicted future spot. . .

. . . now. peter and i have shared a couple of beers [ok, he had beers, i had some moraga cause i'm trying to kid myself about the atkins] and gone round and round on this.

i always talked about implied variance swaps in terms of commodities and what this variance risk premia says about convience yield of commodities, and and does it say anything about how forward is 'gonna converge to spot?

or alternativly, does the difference in the skews of the distributions implied by the option of forward months give me a clue about where forward start options are gonna be. i.e. if option on Dec 2005 crude has implied vol 32%, does that mean i expect Dec95 future to have a constant vol of 2%/day from now to the end up the year, or do i expect Dec95 to bounce around at 1% vol during the months of Jan/feb/mar, and something like 4%/day during october?

actually, i NEVER talked about variance risk premia, i always talked about the distribution implied from the options prices; like variance/covariance swaps, variance risk premia are just a mapping of the implied distribution. [my interest in variance/covariance swaps stemmed from my noodling around with crack/spread options]

peter wanted to look at equities, his math does hold up, [like i was ever gonna beat him on math], and he can construct a variance swap, better than i can [i worked covariance swaps out on a bivariate binomial tree, peter managed to do it in semi-closed form, he's smarter than i am]

and so all the math works, i just think he is solving, maybe not the wrong problem, just one that is uninteresting [to me]

2. Cross-Industry Momentum by Lior Menzly, Oguzhan Ozbas

Abstract:

Industries related to each other through the supply chain (upstream or downstream) exhibit strong cross-momentum. A trading strategy that consists of buying (selling) industries with large positive (negative) returns to their upstream industries over the previous month yields an annual premium of more than 6 percent and a Sharpe ratio of 0.7. While these findings are difficult to reconcile with traditional models of asset pricing that assume unbounded investor rationality, they are consistent with limited information models that predict slow and gradual diffusion of information across segmented markets.

My take:

The authors claim to find "positive cross-correlation among industries that are related to each other through the supply chain. Based on inter-industry flow of goods and services from the Input-Output Benchmark Survey of the Bureau of Economic Analysis, we find that related industries (upstream and downstream) lead industry returns".

The industries are as defined by the SIC code on the CRSP tape (which in my experience is not as good a classification as one might wish, but it will do). Market-value weighted industry returns are computed monthly. Then Upstream (downstream) returns for industry i are computed as the returns of a portfolio of industries that buy (sell) from (to) industry i weighted by between-industry volume of commercial transactions reported in the BEA Survey. Sixty five industries were used.

The returns for this study are from July 1963 to December 2002, although the BEA industry survey is from 1987. Thus there is a look-forward problem in the study and the results could not have been obtained prospectively by a real investor. The authors realize this and try to defend themselves: "Even if there were surveys before the beginning of our sample period in 1963, it is unlikely that they would have differed significantly from the 1987 survey". But the problem is potentially serious.

"Our trading strategy consists of ranking industries into five bins [at the beginning of a month] based on returns in their upstream or downstream industries in the previous month". [We construct] "portfolios that buy industries in the high bin and sell industries in the low bin." This strategy (value weighted) returns a premium of about 6% a year.

"We interpret these findings as suggestive of slow and gradual diffusion of information across informationally segmented markets."

3. Stock Returns, Aggregate Earnings Surprises, and Behavioral Finance by Jonathan Lewellen, S.P. Kothari, Jerold B. Warner

My take:

A lot of academic research has focused on the relation between individual company stock prices and individual company earnings (and earnings surprise). Value Line, Zacks, Starmine have co-discovered or copied these ideas. A separate question is the relation between the overall (S&P 500) stock price level and the aggregate (economy wide) earnings. This paper focuses on the latter (the aggregate level).

The authors duplicate the finding presented in Chapter . of PracSpec: there is no predictive relationship from aggregate earnings to S&P500 performance. "Our first key result is that aggregate earnings are more persistent than individual firms earnings, yet we find no relation between aggregate returns and past earnings surprises. Thus, unlike at the firm level, there is no evidence of delayed reaction to aggregate earnings news."

"Our second main finding is that aggregate returns and concurrent earnings surprises are negatively correlated. For example, over the last 30 years, stock prices increased 6.5% in quarters with negative earnings growth and only 1.9% otherwise (significantly different with a t-statistic of 2.6)." (The explanation offered is that in a quarter in which earnings go down, the market lowers the rate at which it discounts future earnings to an even greater degree and therefore the S&P goes up).

When I read PracSpec I was initially thoroughly confused by these findings because I had done a lot of reading on individual-stock earnings response. For such people the authors add "We emphasize that the negative reaction to [contemporaneous] aggregate earnings is entirely consistent with a positive reaction to firm earnings (and, in fact, we find a positive correlation between firm-level returns and earnings in our sample). The economic story is simple. Firm earnings largely reflect idiosyncratic cash-flow news, unrelated to discount rates. Aggregate earnings are more closely tied to macroeconomic conditions and, therefore, correlate more strongly with discount rates (assuming that discount rates are driven primarily by macroeconomic conditions). Thus, it is not surprising that the confounding effects of discount rates show up only in aggregate returns. Put differently, cash-flow news is fairly idiosyncratic while discount-rate changes are common across firms. By a simple diversification argument, discount-rate shocks should play a larger role at the aggregate level. In short, our results provide a logically consistent picture of market behavior in which discount rates (and discount rate changes) explain an important fraction of [aggregate] stock market movements."

I remember a phrase from my first Economics class: "the fallacy of composition"; what is true about about an individual is not necessarily true about a group. The lesson here is that the earnings of individual firms and the aggregate earnings of the economy do not behave the same and need to be analyzed separately.

4. The Cross-Section of Volatility and Expected Returns, by Andrew Ang, Robert Hodrick, Yuhang Xing, Xiaoyan Zhang

They compute two Beta coefficients for each stock. The first, Beta-Market, is the usual sensitivity of the stock to the market (S&P500), the second Beta-Delta-VIX, is the sensitivity of the stock to changes in VIX. (The cognoscenti will recognize this as a standard linear two-factor model of returns). Stocks with high Beta-Delta-VIX are those that do well on a day that VIX goes up.

Let us think about High Beta-Delta-VIX stocks for a moment. On a day when the S&P is down a lot and the VIX is up, these stocks do better than would be expected from their Beta-Market alone. They don't go down as much as other stocks or even go up.

Now the empirical finding. From January 1986 to December 2000 stocks are divided into quintiles each month based on their Beta-Delta-VIX. Stocks with higher Beta-Delta-VIX tend to have lower average returns. For example the spread between the quintile with the lowest and the quintile with the highest Beta-Delta-VIX is -1.05% per month.

Does this make sense and what does it mean? It suggests that volatility risk is a priced risk-factor. People who want to "insure" themselves against bad returns on VIX-up days can hedge themselves by overweighting High Beta-Delta-VIX stocks in their portfolio, but in so doing they will lower their long term returns. This "insurance" comes at a price. (A finding that is consistent with some index-option research as well).

The second part of the paper is concerned with stock-specific (or 'idiosyncratic' or 'non-diversifiable' risk). This time a three factor Fama-French model of returns is applied and the idiosyncratic volatility is defined as the standard deviation of the residual from that model. Again 5 portfolios are formed each month, but this time based on idiosyncratic vol.

The difference in returns between quintile 1 (low idiosyncratic vol) and 5 (high idiosyncratic vol) is a very large -1.06% per month. This finding is somewhat difficult to explain. In particular it does not seem to be related to the Beta-Delta-VIX effect found in the earlier part of the paper or to other known anomalies.

There does not seem to be a simple intuitive explanation for the low return on highly idiosyncratic stocks AFAIK.

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For more writings by Alex Castaldo