Financial Markets Efficiency and Economic Behaviour

According to the efficient markets hypothesis security prices should value information available to economic agents. An essential interpretative concept is the notion of no arbitrage. When there is no arbitrage, market returns should not be predictable. Several forms of efficiency can be identified, according to the type of information set used in the formation of expectations. In static return regressions the conditions for financial markets efficiency are not fulfilled, since there is evidence of return predictability in both the stock and housing markets. In a behavioural perspective this outcome could be the result of agent cognitive limits, due to the use of heuristic rules. Representativeness, availability and anchoring could determine under- or overvaluation of existing assets with respect to fundamental value. An important further aspect regards the proper use of prior information. The expectations hypothesis concerns the relations between the yields of fixed income securities with different term. While static spot rate spread regressions provide evidence of return extrapolation, as for the stock and housing markets, forward rate regressions confirm the predictions of the hypothesis, an outcome that may be related to their dynamic properties.

In the earliest descriptions of the efficient markets hypothesis asset prices were modelled as a martingale. A martingale is a stochastic process with the fundamental property, that the current price is equal to the conditional expectation of the price in any future period. As a consequence, the price in any time period is equal to a cumulative sum of an initial condition and random disturbances. Therefore, its volatility increases linearly with time. More generally, when there is no arbitrage in the security market, the stock price in the current period is equal to the expected present discounted value of the subsequent period payoff, conditional on information available to economic agents. The definition of the stochastic discount factor follows from the linearity properties of the asset pricing function. When there exists a riskless asset, the conditional expected value of the stochastic discount factor is equal to the inverse of the riskless gross return. In the equivalent risk-neutral valuation expectations are taken with respect to an equivalent martingale measure.

The equity premium is the excess rate of return of stocks over the riskless rate. The assumption of log-normality for gross asset returns implies, that the conditional expected excess rate of return is equal to the opposite of the covariance between the natural logarithm of the stochastic discount and the stock rate of return. The Sharpe ratio, modelled as the ratio between the expected excess rate of return and its standard deviation, defines a volatility bound for the stochastic discount factor. The monthly real excess return has been equal on average to 8.8 per cent at a yearly rate in a panel of 403 stocks for the five largest Euro area economies in the 2012m02–2015m06 sample period and its standard deviation is about ten times as large. Further estimates of the volatility bound can be obtained from the within and between components and provide evidence on the completeness of financial markets. The capital asset pricing model relates the excess return of stocks over the riskless rate to the excess return of the market portfolio.

The equivalent risk-neutral valuation implies, that investors should not expect to earn more than a normal return in the stock market. We assess this prediction with a static regression framework, using stock market data for the five largest Euro area economies. In order to account for unobserved heterogeneity, we employ either first differences and orthogonal deviations transformations or an error components approach to estimation. While the dividend growth rate does not have explanatory power, the log dividend/price ratio is positively and significantly correlated to subsequent real gross return rates and its estimated coefficient increases linearly with the forecasting horizon. Following a behavioural interpretation these outcomes show asset prices are not correctly valued, because according to the efficient markets hypothesis the log dividend/price ratio should anticipate future dividend growth rates, rather than subsequent returns. Cognitive science suggests, that rational agents form expectations on the basis of heuristic rules to make financial decisions. Representativeness, availability and anchoring may result in either under- or overvaluation of existing assets. An important aspect of the process of expectations formation is related to the application of Bayes’ rule.

The two main forms of fixed income securities are discount, or zero-coupon, and coupon bonds. The term of a bond is its time to maturity. Discount bonds make a single payment at maturity. The yield to maturity is the discount rate that compounded makes the bond purchase price equal to its face value. Coupon bonds make payments at regularly spaced intervals until maturity. The yield to maturity of a coupon bond is the discount rate that equates the bond purchase price to the present discounted value of coupon and principal payments. The holding period return is the return obtained holding a bond for a period of time shorter than the term. The duration of a bond is a function of coupon and principal payments and measures the elasticity of the purchase price with respect to the gross yield. The tax structure on various capital income components determines a bond pricing.

The term structure of interest rates is the relation between the yields of fixed income securities with different maturity. The securities used to compile the yield curve are normally government bonds. The expectations hypothesis states that long rates should be equal to expected average forthcoming short rates. Moreover, forward rates should reflect expectations of future spot rates. Forward rates result from trade between short and long term bonds and are either greater or lower than the spot rates with the same term, when the yield curve is respectively upward or downward sloping. The rollover term premium is the difference between the long rate and expected average short rates, conditional on information available in any time period. The holding period term premium is the difference between the expected holding period return and the spot rate. The forward term premium is the difference between the forward rate and the expected future spot rate.

The term spread is defined as the difference between long and short rates and models expectations of forthcoming changes in short rates. As a consequence, a modified version of the spread should be positively correlated to the change in the long rate over the short term for a given maturity, with a regression coefficient equal to unity. Static yield curve regressions for the Euro area in the 2004m09–2018m08 sample period show that the term spread predicts holding period returns, rather than changes in long rates, since estimated slope coefficients are negative. The yield curve regression findings provide evidence of return extrapolation of Euro area investors in the formation of expectations on the term structure of interest rates. A behavioural interpretation of return extrapolation is based on the heuristic rules framework. Similarly, the difference between forward rates and current spot rates should be positively correlated to changes in spot rates over the forward rate horizon. In forward rate regressions the slope coefficient estimates are consistent with the expectations hypothesis. A distinguishing feature of the forward rate regressions is their well-defined dynamic structure.

In the real estate market, the no arbitrage condition defines a relation between the housing price in the current period, the rent and the subsequent period price. The housing premium is the excess housing rate of return over the riskless rate. The quarterly real housing excess return has on average been greater than 10 per cent at a yearly rate in Italy in the 1996q01–2020q04 sample period and its standard deviation is of the same order of magnitude. The housing Sharpe ratio provides further evidence on the completeness of financial markets. In forecasting regressions the natural logarithm of the rent/price ratio is positively correlated to forthcoming real housing excess returns and housing return volatility at horizons of 4, 8 and 16 quarters. Rational speculative bubbles may explain housing price volatility, although they do not entail return predictability. A behavioural approach considers the implications of under- and overreaction to news regarding fundamental value, due to the use of heuristic rules. The two most common forms of mortgage contracts are adjustable and fixed rate mortgages.

A derivative is a security whose price is a function of the value of an underlying asset. Derivative securities provide insurance from different types of risk. Futures are similar to forward contracts and settle payments for delivery at future dates. The assumption of no arbitrage in futures and forward markets implies, that the corresponding prices have a random walk property. Futures and forward contracts protect investors from price fluctuations. Options are contracts that give the right to buy or sell an activity for a defined price at some date in the future and insure from asset price volatility. Swaps are contracts that regulate the exchange between different flows of payment. Interest rate swaps trade flows with different maturity, in order to diversify interest rate risk. Exchange rate swaps trade flows in different currencies, to hedge against exchange rate volatility.

Following the efficient markets hypothesis activity prices are determined conditionally on the type of information valued by investors. The equivalent risk-neutral valuation predicts that investors should not expect to earn more than normal returns, whereas in static predictive regressions for the asset and housing markets valuation ratios are positively correlated to forthcoming returns. A cognitive science view suggests, that price under- or overvaluation could occur, when agent expectations are formed on the basis of heuristic rules. The expectations hypothesis states, that long rates should equal expected average short rates and forward rates should model expected future spot rates in the market for fixed income securities. In static spot rate spread regressions the term spread forecasts holding period returns. Conversely, forward rate regressions have a well-defined dynamic structure and confirm the predictions of the hypothesis. Finally, the volatility properties of the stochastic discount factor can be interpreted as evidence regarding the completeness of financial markets.