Incremental Volatility Research Articles

Incremental Volatility and Related Portfolio Analytics

In this article, the authors prove a simple formula to compute the incremental volatility, that is, the change in the portfolio volatility due to the removal of one asset from the portfolio. The common practice adopted in the literature and in the industry is to avoid the full recalculation of the portfolio volatility and to use a first-order approximation based on the gradient of the portfolio volatility. Here, the authors introduce a new exact formula that does not require recomputing the volatility of the new portfolio but exploits quantities computed previously. Using the new formula, they can easily compute the effect on the portfolio volatility of any arbitrary change in the weight of one asset as well as to determine the optimal trade, that is, the weight change that allows the maximum reduction in the portfolio volatility. A simulation exercise and an empirical analysis illustrate the clear advantage, in terms of accuracy, saving in computational time and calculation of portfolio analytics with respect to the full reevaluation and the commonly used linear approximation. Due to their striking simplicity, the new formulas provide important portfolio analytics of immediate use in the asset management industry.

Incremental Volatility and Related Portfolio Analytics

In this note we prove a simple formula to compute the Incremental Volatility, i.e. the change in the portfolio volatility due to the removal of one asset from the portfolio. The common practice adopted in the literature and in the industry is to avoid the full recalculation of the portfolio volatility, but rather to use a first order approximation based on the gradient of the portfolio volatility. Here, we introduce a new exact formula that does not require to recompute the volatility of the new portfolio, but exploits quantities computed previously. Using the new formula, we can easily compute the effect on the portfolio volatility of any arbitrary change in the weigth of one asset as well as to determine the optimal trade, i.e. the weight change that allows the maximum reduction in the portfolio volatility. Due to their striking simplicity, the new formulas provide important portfolio analytics of immediate use in the asset management industry.

Keine erhöhte Volatilität auf Agrarmärkten durch Optionshandel

Der Handel mit Optionen gewinnt auf volatileren Agrarmarkten zunehmend an Bedeutung. Nun stellt sich die Frage, ob der Optionshandel ein sinnvolles Instrument zur Risikoabsicherung von Landwirten und Landhandlern darstellt oder ob er vielmehr ein Treiber der Agrarpreisvolatilitat ist. Die Autoren schliesen aus okonometrischen Schatzungen am Beispiel des MATIF-Kornermaismarktes, dass der Optionshandel die Volatilitat nicht erhoht.

The volatility of comprehensive income and its association with market risk

AbstractFinancial statement preparers claim that the ‘excess’ volatility of comprehensive income (CI) confuses financial statement users. We examine the volatility and risk relevance of CI, relative to net income, for a sample of 92 New Zealand nonfinancial firms for the period 2003–2010. The results show that CI is more volatile than net income. However, the volatility of CI incremental to net income is not related to market risk. Furthermore, the incremental volatility of CI does not modify the pricing of net income. These results hold when asset revaluations are excluded from other CI.

Risk Relevance of Comprehensive Income

We examine the volatility and risk relevance of three income measures: net income, comprehensive income, and comprehensive income adjusted for asset revaluations for a sample of 79 New Zealand non-financial firms from 2003-2008. Comprehensive income is more volatile than net income and adjusted comprehensive income. There is a strong positive correlation between the three income volatility measures and market risk. However, the volatility of comprehensive income incremental to net income is not related to market risk. Furthermore, the incremental volatility of comprehensive income does not modify the pricing of net income. The results have policy implications for the IASB.

Volatility and Risk-Relevance of Comprehensive Income

In this paper, we investigate the volatility and risk-relevance of the standard deviation of two reported income measures; net income and comprehensive income for a sample of U.S non-financial firms over the period 2005-2010. We find that comprehensive income is more volatile than net income. We also find a positive correlation of the two income-volatility measures with volatility of stock returns and beta. Moreover, the incremental volatility of comprehensive income does not provide market-risk relevant information beyond net income. Further, the incremental effect of the volatility of comprehensive income is not priced beyond the volatility of net income. Alternatively, the incremental volatility of net income is priced beyond the volatility of comprehensive income. We use reported figures for all the components of other comprehensive income and comprehensive income. Our results support the claim that comprehensive income is more volatile than net income and may not be a better proxy for firm’s performance.

Hedging Long-Duration Liabilities with LeveredShort-Duration Bonds

The term premium per year of duration declines with an increase in bond maturity due to an excess demand for long-duration bonds. Rather than holding the liabilityimmunizing long-duration bond, therefore, investors can capture a higher return by leveraging short-duration bonds to get the same dollar duration as the liability. This strategy would have generated between 0.40% and 0.90% of incremental annual returns over the last 56 years, depending on the liability profile. The mismatch in asset and liability maturities also exposes the investor to volatility, with lower (negative) returns when the yield curve flattens and higher returns when the yield curve steepens. The incremental volatility from this mismatch is small for plans with equity allocations, however, and even partly offsets large equity drawdowns as Fed action causes a steepening of the yield curve. A levered short-duration strategy thus can be an important tool for underfunded plans as they seek increased returns and improved efficiency relative to plan liabilities.

The impact of stock incremental information on the volatility of the Athens stock exchange

In this paper we model the volatility of the Athens Stock Exchange general index. With the use of alternative conditional heteroskedasticity models (Glonsten et al., 1993; Bollerslev, 1986; Zakoian, 1991) we investigate whether stock returns include incremental information when we model index volatility. Whereas empirically much is known about the volatility of the Athens General Index, very little has been done on the impact the stock increments have on the General Index volatility. Our econometric approach relies on the comparison between TARCH and modified GARCH estimation techniques, on a sample of 48 shares included in the Athens General Index, using daily data over the period 1993–2003. After capturing for any possible qualitative effects, such as the cut-off points indicating a “bearish” or “bullish” capital market, the results clearly indicate that the shares include incremental volatility information in their returns.1 1 An earlier version of this paper was presented at the 2nd Meeting of the Hel...

Risk-Relevance of Fair-Value Income Measures for Commercial Banks

We investigate the risk relevance of the standard deviation of three performance measures: net income, comprehensive income, and a constructed measure of full-fair-value income for a sample of 202 U.S. commercial banks from 1996 to 2004. We find that, for the average sample bank, the volatility of full-fair-value income is more than three times that of comprehensive income and more than five times that of net income. We find that the incremental volatility in full-fair-value income (beyond the volatility of net income and comprehensive income) is positively related to marketmodel beta, the standard deviation in stock returns, and long-term interest-rate beta. Further, we predict and find that the incremental volatility in full-fair-value income (1) negatively moderates the relation between abnormal earnings and banks' share prices and (2) positively affects the expected return implicit in bank share prices. Our findings suggest full-fair-value income volatility reflects elements of risk that are not captured by volatility in net income or comprehensive income, and relates more closely to capital-market pricing of that risk than either net-income volatility or comprehensiveincome volatility.

Modelling S&P 100 volatility: The information content of stock returns

Theoretical models that relate volatility to the quantity of information are extended to a multi-asset setting and it is deduced that stock returns may or may not have incremental information when modelling index volatility, depending on the sources of information that move stock prices. The first empirical study that can help resolve this theoretical uncertainty is presented. A detailed analysis of the daily volatility of the S&P 100 index from 1984 to 1998 shows there is some incremental volatility information in the returns from the 100 shares that define the index. This evidence is obtained from ARCH models that incorporate leverage effects, dummy variables for the 1987 crash and aggregate measures of stock return volatility. Significant differences between estimated volatilities are found for various stock measures and sub-periods.

The incremental volatility information in one million foreign exchange quotations

The volatility information found in high-frequency exchange rate quotations and in implied volatilities is compared by estimating ARCH models for DM/$ returns. Reuters quotations are used to calculate five-minute returns and hence hourly and daily estimates of realised volatility that can be included in equations for the conditional variances of hourly and daily returns. The ARCH results show that there is a significant amount of information in five-minute returns that is incremental to options information when estimating hourly variances. The same conclusion is obtained by an out-of-sample comparison of forecasts of hourly realised volatility.

Fair value accounting: Effects on banks' earnings volatility, regulatory capital, and value of contractual cash flows

We investigate fair value accounting critics' assertions by restating earnings and regulatory capital to reflect banks' disclosed investment securities fair values. We find: (1) Fair value-based earnings are more volatile than historical cost earnings, but share prices do not reflect the incremental volatility. (2) Banks violate regulatory capital requirements more frequently under under fair value than historical cost accounting. Fair value-based violations help predict regulatory capital violations, but share prices do not reflect this potential increased regulatory risk. Only historical cost violations are market information events. (3) Share prices reflect interest rates changes, even though investment securities' contractual cash flows are fixed.