New perspectives on the axiomatic framework of asset pricing

Abstract

Two identities are very influential to asset pricing theory: the no arbitrage condition and the Campbell-Shiller decomposition of valuation ratio. The no arbitrage condition could be seen as a weak and necessary condition for market efficiency; the Campbell- Shiller decomposition is based on an accounting identity that all asset pricing models shall satisfy. The axiomatic feature of those two frameworks make them very attractive to work with. This thesis derives some axiomatic results based on those two frameworks for three different asset classes: stock market index, government bond portfolio and FX rates, and shows that those results have the potential to bring some new empirical insights to classic questions in asset pricing theory. In the first chapter, we first derive a new valuation ratio decomposition that is related to the Campbell and Shiller loglinearization but that resembles the Gordon growth model more closely and has certain other advantages. In the second part of first chapter, we introduce a volatility index that provides a lower bound on the market’s expected log return. Combining those two ingredients, we define a sentiment indicator based on option prices, valuation ratios, and interest rates. The indicator can be interpreted as a lower bound on the expected growth in fundamentals that a rational investor would have to perceive to be happy to hold the market. The bound was unusually high in the late 1990s, reflecting dividend growth expectations that in our view were unreasonably optimistic. In the second chapter, we log-linearize the government’s debt portfolio budget constraint using a novel pair of valuation ratios: tax-to-debt and spending-to-debt. We show that splitting the tax and spending channels of primary surplus has several theoretical advantages as well empirical ones. For example, it helps to capture the correct dynamic of surplus process without adding any latent variable into the framework. It also empirically explain the variation of inflation quite well both in-sample and out-of sample. Profession forecaster is a ‘hard to beat’ benchmark when it comes to inflation forecasting. The preliminary empirical work shows the dual valuation ratios, i.e. the tax-to-debt and spending-to-debt ratios, perform well comparing to the forecasts. The third chapter has two parts. In the first part, we consider log-linearization of a nation’s external account imbalance. The novelty is to split the external account into two different channels: import and asset holding; export and liability issuing. We show that the two valuation ratios raised from the two channels are empirically relevant when jointly explaining the time variation of dollar strength. In the second part, we try to measure the ex-ante risk premiums of FX rate returns using options of FX rate and stock index. As a side product, propose a index that measures the difference between risk-neutral and real-world expectations by comparing option implied risk-premium and the consensus of professional forecasts through the lens of no-arbitrage condition for exchange rate returns. This simple enchmark can be interpreted as the time varying risk aversion of an unconstrained representative investor with CRRA utility whose entire wealth is invested in the market.