Measures of monetary policy rate uncertainty significantly improve forecasting models for equity volatility and variance risk premia. Theoretically, there is a strong link between the variance of equity returns in present value models and the variance short-term rates. For example, there is natural connection between recent years’ near-zero forward-guided policy rates and low equity volatility. Empirically, the inclusion of derivatives-based measures of short-term rate volatility in regression forecast models for high-frequency realized equity volatility has added significant positive predictive power at weekly, monthly and quarterly horizons.

*The post ties in with SRSV’s lectures on non-conventional monetary policy and implicit subsidies, particularly the part on variance risk premia.*

*The below are excerpts from the paper. Emphasis and cursive text have been added. *

### The trouble with explaining equity volatility

“[*For*] forecasting equity return volatility…the standard set of short-term predictive factors should contain [i] variables capturing volatility persistence, like lagged realized volatility…[ii] forward-looking variables representing market views about future realized volatility, like equity implied volatility…and [iii] variables capturing asymmetric nature of volatility, like negative returns. However, none of these variables can actually explain the underlying sources of changes in equity return volatility.”

“The question ‘Why does equity market volatility change over time?’ has remained largely unanswered [*in the empirical academic literature*]. The main reason is the simple fact that __fundamental economic variables are only available at low frequency – monthly or quarterly – while equity volatility changes even on a daily basis__.”

### The theoretical link between policy rates and equity volatility

“Given that the monetary policy (i.e. short-term risk-free) rate is a key factor for pricing many securities and derivatives, __there should be a strong link between monetary policy rate uncertainty and equity return volatility__. Moreover, this link should be observed not only in the longer term. Indeed, according to basic present value models, the variance of equity prices is directly linked to the conditional variances of future discount rates, which are, in turn, the explicit functions of expected risk-free interest rates and risk premia.”

“Intuition…can be gained by examining the one period expected [*equity*] return within the conditional CAPM [*capital asset pricing model*]…__The variance of risk-free rate [ affects the variance of the equity return] one for one and so has a large effect__. In particular…the variance of the risk free rate accounts for approximately 65% of the variance of the return for neutral stocks and for up to 71% for value stocks…The impact of the variance of market beta is substantially lower…The impact of variance of market price of risk for one period returns is also large and at a par with that of risk-free rate variance. However, it becomes smaller for longer horizons if the shocks to market prices of risk are less persistent than shocks to interest rates.”

“Given that short-term interest rates are set directly by monetary policy, __the uncertainty about the future course of short-term interest rate represents the uncertainty about the expected path of Federal Reserve monetary policy__…Therefore, the short-term interest rate volatility should be a sign of monetary policy rate uncertainty”.

### The empirical evidence on policy rates and equity volatility

“We show that __variables capturing monetary policy rate uncertainty have important predictive power for short-term equity return volatility forecasts__… Consistently with the theory, monetary policy rate uncertainty is positively and significantly related to uncertainty in equity markets.”

“The concept of `realized volatility’ [*for equity returns*]…is based on using high-frequency data and provides a more precise estimate of the daily volatility of asset returns. The idea is simple: the __daily realized volatility of a single asset return is measured via the sample variance of high frequency data__, such as 5-minute returns data… We estimate realized variances from squared 5-minute intraday returns. We use daily realized variance of 5 minute returns data from the underlying equity indices, as published by the Oxford-Man Institute…Data on realized variance for S&P 500 is available from 3 January 1996, for FTSE 100 – from 21 October 1997, and from 3 January 2000 for Euro Stoxx 50.”

“We use an empirical method of regression-based projections of realized [*equity return*] variance over weekly, monthly, and quarterly horizons on the prior information set comprising__ a standard set of predictive variables__. These include lagged realized variance components, most recent return variance realisations, negative return shocks, and lagged squared option-implied volatility. We __then add forward-looking proxies of monetary policy rate uncertainty__ available at high (daily) frequency.”

“To obtain monetary policy rate uncertainty proxies…at high frequencies, we refer to financial markets data… __For our main proxy of monetary policy rate uncertainty, we use squared 3-month implied volatility from at-the-money options__ on 3-month interest rate futures. The data are from a relatively liquid market of exchange traded call and put options on 3-month Eurodollar and Short Sterling futures, which are calculated on LIBOR at settlement, and 3- month Euribor futures, which are relatively liquid exchange-traded instruments based on Euribor…Market prices on options on short-term interest rate futures imbed market views (forecasts) of volatility of underlying interest rate over the life of option.”

“We show that the __proxies for monetary policy rate uncertainty have a significant and positive predictive power for the short-term equity return variance__…at weekly, monthly and even quarterly horizons… By including a monetary policy rate uncertainty proxy, we improve the forecasting performance of available models of conditional variances and volatilities of international equity indices’ returns. The gains are obtained at weekly, monthly and even quarterly horizons.”

“Indeed our results imply that __the low level of equity volatility during 2013-2014 partially reflected lower uncertainty about short-term interest rates__…Low monetary policy rate uncertainty may have resulted from unconventional monetary policies, such as forward guidance and quantitative easing.”