In order not to be consumed by historical reflection, the second chapter extends this work with some new results on lack of arbitrage, which unify much of the research in this area by relying on neoclassical consumer theory. The second chapter is technically more demanding than the rest of the book and can be safely skipped by the reader who is prepared to accept his results, used in the third chapter. While some may object to this chapter as an overly harsh indictment of the behavioral school of financial thinking, I must confess that it still represents much of my own thinking on the subject.
There is not enough space here to comment on all the people who have influenced me. Needless to say, the rest of the seminar had a hard time living up to that expectation.). Dick's mastery of the basic intuitions of finance and his clarity of vision remain indicators for me to this day.
Bob defined much of the analytical framework that is the basic kitbag of modern finance; Myron, Fischer and Bob started with their incredible insight – encapsulated in the Black-Scholes model – one of the great historical explosions in research.
NO ARBITRAGE
THE FUNDAMENTAL THEOREM OF FINANCE
Research into the implications of NA is the meat and potatoes of the modern financial world. It follows that the value is simply the discounted expected value of the final payout, assuming that the stock price deviation is the risk-free rate. Similarly, we could construct a replicating portfolio composed of the risk-free rate and the stocks whose returns are locally identical to the return on the call option.
NA in the form of LOP requires that the portfolio as a risk-free asset has a unique risk-free rate of return, r. Through NA, this would force the value of the option to be the original cost of such a portfolio. The famous Modigliani-Miller (MM) theorem (Modigliani and Miller 1958) about the irrelevance of a firm's financial structure to firm value.
Note that the equity claim is simply a call on the company's value with an exercise price equal to the sum of the face value of the debt claims.
BOUNDING THE PRICING KERNEL, ASSET PRICING, AND COMPLETE MARKETS
An important interpretation of the kernel is that it is the ratio of marginal utilities at different levels of welfare. The debate is reminiscent of the old discussion about the equalization of factor prices in the pure theory of international trade. One way to interpret the literature on bounding kernel volatility is that it provides an alternative way to characterize Φ.
If U is a monotonic concave utility function (differentiable as required), then the agent chooses from portfolios, α, of the marketed assets. The comparison between problems 1 and 2 provides all the limits now available in the literature. Loosely speaking, an upper bound on the variability of the price kernel is a statement about how close certain opportunities can be to arbitrage opportunities.
An upper bound for the volatility of the price kernel From our previous two theorems, agents prefer kernels to be volatile, and more risk-averse agents require more volatility. It therefore follows that any upper bound on the variability of the price kernel will be intimately related to an upper bound on the risk aversion of the marginal agent. Unfortunately, however, it is not possible to determine an upper limit for the variability of the core from the prices of assets alone.
Since the variability of each kernel can be increased without affecting price, price considerations alone cannot place an upper bound on the volatility of the allowed kernels. Our fundamental analytical tool will be the following relationship between the relative risk aversion and the volatility of the associated kernels. The implication is therefore that the foregoing appears to be within an order of magnitude of a conservative estimate of the upper limit of risk aversion for the market.
In both cases, we now have the ability to limit the volatility of the pricing kernel by calculating a market risk aversion limit. The claim of a limit to the risk aversion of the marginal investor is simply a statement about the desirability of an investment in the market at the margin.
APPENDIX
In fact, we could have performed exactly the same calculations with a bilinear utility function and achieved very similar results. Neither does any of the above rest on the false belief that a high Sharpe ratio is the same as an arbitrage opportunity.7 It is not, since a high variance and, therefore, a low Sharpe ratio can come from a highly skewed report. positive result and that would be good, not bad. Rather, our analysis is consistent with the parametric assumptions we have made, namely that the marginal utility function is uniformly bounded above risk aversion, and the analysis is specifically designed to serve as a pragmatic guide to the problems we. will be examined in the next chapter.
For an agent with an initial wealth of ω and a constant risk aversion coefficient of R, facing a core φ with a volatility of σ2, the optimal utility is . This implies that the indifference curves on which utility is held constant as ω and σ change are curves on which. If we let a market average price of risk, Rw, set the volatility of the core, then we have that from the previous results.
The increase in wealth that would equal this increase in volatility for an agent with a risk aversion of R would be.
EFFICIENT MARKETS
A market is said to be weakly form efficient if St contains all the past prices of the asset, that is, if. Proposition 1: If Stdenotes the market information set, then the value of any investment strategy that uses an information set At⊆St is the value of the current investment. From weak form efficiency, L(pt−) is a subset of the market information set, and again by applying Proposition 2, it pays off.
In general, for any information set, At, that is a subset of the market information set and that contains the risk-free asset, we have This observation has led to something bad in testing the efficient markets hypothesis. Fortunately, however, the price kernel volatility bounds developed in the second chapter hold the possibility of separating these two hypotheses.
This is consistent with the hypothesis that the market is efficient, and thus a confirmation of the hypothesis. Not only does the market seem to incorporate all of the Weather Bureau's information, it actually seems to know a bit more. Note that the stock appears to have rallied on the day of the announcement, but that's only the beginning of the story.
If, based on the results of the second chapter, we indicate for the marginal investor the correct variance or variance that is tied to the volatility of the price core. If we let R2 denote the R-squared of the regression of the return on the information set, we now have a nice result. Since there is certainly no shortage of ingenuity among participants in the financial market, I suspect there is a lack of interest.
More interesting, however, is to assume that the efficient market holds and that all serial correlation is captured by the change in expected return. Proposition 6: In the case where all lagged correlation coefficients are the same β, then the minimum value of the coefficients is subject to the constraint that. In other words, if the market were efficient and if all predictability were captured in the mean, the hundred-day volatility could easily be consistent with that found in the data.
A particularly intriguing class of efficiency tests are direct tests of fund managers' ability to outperform the market.
A NEOCLASSICAL LOOK AT BEHAVIORAL FINANCE
THE CLOSED-END FUND PUZZLE
However, one case where the fundamentals seem unequivocal is that of the closed-end funds. This implies that our portfolio's value will remain a constant part of the NAV of the fund. From proposition 1, a (permanent) increase in the payout lowers the value of the driver's fee and therefore reduces the discount.
The fund's total holdings are n shares, and the NAV is therefore given by A=nS. Since the discount is the value of the manager's fees, we can write this as. For a number of the funds, data was only available for a subset of this period.
This increases the denominator of the formula by the excess of the fees over the management fees. This is the incremental value that will be added over and above the NAV of the fund. They can either commit funds at the time of offering, or they can wait until the fund trades in the aftermarket.
More generally, the discount is a function of capital gains history, which investors use to project the actual capital gains policy. With the linear adjustment of the current capital gain to the current discount, the equilibrium determines the discount and the capital gain as given in statement 4. Specifically, let the total payout including the fee and the dividend flow be given by
What about the features of the discount time series, that is, the life cycle of Figure 4.1. More importantly, we should expect the properties of the discounting time series to depend sensitively on how capital gains outflows are modeled. The fee-based deduction depends on the respective payments received from fund operators and investors.
Note: This table reports the results of stacked annual regressions of the change in discount (where discount is defined as (NAV(i,t)-Price(i,t))/NAV(i,t)).
