Financial Market Efficiency



Financial Market Efficiency

Question 5)

In the context of variance bounds and other tests based on spot yields, for bonds, define the perfect foresight long rate and its theoretical relationship with the actual long rate under rational expectations. How can regression analysis be employed to show that there is a relationship between this theoretical long rate and the actual long rate?

In widely cited research into the question of bubbles and irrational behavior in financial markets, Robert Shiller (1981) has suggested that stock market prices clearly exhibit excess volatility compared to their fundamentals. He has recently updated his research up to 2000 in his book Irrational Exuberance. The results are similar to his 1981 findings and are used to discredit the 1990s boom in U.S. and worldwide stock prices. According to economic theory, the stock price should equal the expected value of dividends. However dividends are very stable; they ?uctuate very little about an upward trend. Expected dividends should therefore also ?uctuate little, and consequently stock prices should be stable Whatever the merits of arguments in favor or against the 1990s boom in technology stocks, the variance-bound test as implemented by Shiller and many others is a fallacy.

The expectations theory of the term structure implies that the spread between a longer-term interest rate and a shorter-term interest rate forecasts two subsequent interest rate changes: the change in yield of the longer-term bond over the life of the shorter-term bond, and a weighted average of the changes in shorter-tenu rates over the life of the longer-term bond.

Since individuals live more than one period and since money balances carry over from one period to the next, individual's decisions in any particular period are influenced by what they think that their current money balances will be worth in future periods. Thus, a model of how individuals form their expecta- tions regarding the future behavior of prit:es is an essential part of our analysis. Many different models of expectations formation have been discussed in the literature. The particular model which we will employ is a model of 'rational expectations'.' This particular concept has been selected out of the many possible spccirfications of the mechanism of expectation formation. Second, models of 'rational expectations' provide the most appropriate analytical basis for studying the 'optimum quantity of money'. Models vd+ith rational expectations operate like models of compeaitive equilibrium over time in which welfare analysis may proceed along standard lines. In models with other expecta- tion formation mechanisms, the welfare effects of errors of expectations tend to be confused with the welfare,effects of a correctly anticipated inflation. Third, the modei of rational expectations will enable us to study the effect on current price level of an anticipated, future change in monetary policy.

This negative correlation is not, however, statistically signi?cantly different from zero, because the number of independent observations is small. For Shiller's data period 1871-1979, the 5-year time period means that the 109 years of data amount to only 22 independent ...