_{1}

Many banks and commentators argued that fair value accounting was the root caused the procyclical decline in bank assets and capitals, the failures of large financial sector and extreme volatility in financial asset prices during the GFC. Fair value measurements may result in different figures for earnings and capital, both of which are important as buffers against insolvency. Fair value may also convey different messages to the market, either value relevance or volatility, it will lead to different economic consequences in allocating capital resource. This study is an attempt to review the studies of fair value and its impact on earnings volatility and stock price volatility and takes a step further it shows the way in which fair value could potentially introduce volatility into the financial system in particularly a mathematical derivation shows that the government bonds volatility is affected by earnings volatility and its decomposition of fair value and historical cost earnings volatilities. As such, fair value may contribute to a highly volatile market and general investors need to understand the tradeoff between fair value relevance and volatility in making an in vestment decision.

Researchers study the economic consequences of adopting fair value accounting as part of IFRS and find that fair value measures are more value relevant in explaining stock prices. Barth [

Previous studies suggest that share prices reflect a risk premium associated with earnings volatility (Litzenberger and Rao [

In reviewing the US Financial Accounting Standard 133 for derivative instruments, Barton [

Earnings volatility is a particular concern for investors. Market valuation of firms is largely driven by earnings expectation and volatility in earnings is likely to increase investor perceptions of risk in an investment (Bao and Bao [

The effect of fair value accounting has particularly evident in the European capital markets. Armostrong et al. [

International Accounting Standard Board (2003) defines fair value as the price for which an asset could be exchanged, or a liability settled between knowledgeable, wiling market participants in an arm’s length transaction. Thus, fair value is a selling price or exit value in an active market. It is the amount that would be received from selling an asset or transferring a liability in an orderly transaction. The fair value of an asset (or liability) can be derived by a three levels’ hierarchy of inputs: Level 1 inputs, quoted prices available in active markets for identical assets (liabilities); Level 2 inputs, quoted prices for similar assets (or liabilities) that can be observed from the markets; Level 3 estimated as the present value of future cash flows that are associated with assets (or liabilities). A generalized equation will be:

where

Earnings volatility is measured as the standard deviation of aggregate earnings per share of a stock index in any country over a testing period and

where

Debt markets and stock markets are essentially connected. This study predicts that fair value is associated with the overall market volatility, namely, earnings volatility, stock price volatility and specifically government debt volatility. The mathematic derivation of the association between fair value and market volatility is based on the equilibrium relationship between earnings, stock prices and government bond yields. Suppose an investor longs one share, the expected return from investing in this share can be expressed as:

The expected rate of return on share is_{ }and

current period and next period respectively. The return consists of two components, the dividend yield

The equation states that the investor is willing to pay for the share is equal to the discounted value of the dividends and proceeds from selling the share. Same logical can be applied to derive

This is the dividend discount model which states that the current share price depends on all future discounted dividends. If dividends are expected to grow at a constant rate

The model holds true if the rate of return is greater than the dividend growth rate. Replacing dividends in the constant growth dividend model with the payout ratio,

where the growth rate is determined as the retention ratio,

The expected rate of return is usually expressed as the risk-free rate, such as 10-year government bond yield, plus a risk premium required by investors for holding this share. Yardeni [

This is known as the Fed Model which later is used as a simple tool to measure the trade-off between two competing asset classes investment, equities versus bonds. The Fed Model illustrates a substitution effect between equities and bonds: when the stock market’s earnings yield (Earnings per share) is above the long-term government bond yield, investors are better off investing in stocks and they should shift funds from bond markets to stock markets. The opposite should be true when interest rates are high. The Feb Model states that bond and stock market are in equilibrium when the 10-year government bond yield equals the expected earnings yield; the stock market is undervalued (overvalued) when the expected earnings yield is higher (lower) than the 10-year government bond yield. The log form of the Feb Model is:

To find the volatility or variance of the log risk free rate, we can impose a restriction on the weights of two variables in the right-hand side of the equation equal to (1, −1). So, the variance would be:

The above equation suggests that the volatility of government bonds equals the sum of earnings volatility and stock prices volatility, minus two times their covariance. The risk free rate, earnings and prices are all in log forms. Subsequently, when the aggregate earnings are decomposed into fair value and historical cost two components, one can further derive the equation:

Therefore, mathematically we have shown that the government bonds volatility is affected by earnings volatility and its decomposition of fair value and historical cost earnings volatilities, stock price volatility, and the covariance between fair value earnings and historical cost earnings, the covariance between fair value earnings and stock prices, and the covariance between historical cost earnings and stock prices. Using

All the variables are previously defined.

Accounting information plays an important role in healthy functioning of financial systems because an efficient capital resource allocation depends on assessment of firms’ financial position and performance and accounting standards are the key to ensure that firms’ financial position and performance is measured in a way that reflect economic substance, comparable across entities and adequately disclosed. The concept of fair value is a key element in the international accounting standards and its implementation pose serious concerns in terms of financial stability. Fair value measurement is supported on the ground that it provides information which is more relevant to the economic substance and presumably such information will be more useful to investors. However, fair value could potentially introduce volatility into the financial system. A further empirical study will warrant the debate on fair value as to what extent fair value convey different messages to the market, either value relevance or volatility which subsequently leads to different economic consequence in allocating capital resource and for general investors they need to understand the tradeoff between fair value relevance and volatility in making an investment decision.

Mathematically this study has shown that the government bonds volatility is affected by earnings volatility and its decomposition of fair value and historical cost earnings volatilities, stock price volatility, and the covariance between fair value earnings and historical cost earnings, the covariance between fair value earnings and stock prices, and the covariance between historical cost earnings and stock prices. The research design shows an attempt to link the micro aspects of accounting standards and accounting information at firm-level to the macro implications on market-level earnings, stock markets and government debt markets. To achieve this goal, researchers can first apply the principle components analysis to capture an aggregate volatility of fair value accounting information. Manly [