When Policy Becomes Volatility

By 30 April 2025 the S&P 500 stood 1.8 per cent below its 1 April close, and the 10-year Treasury par yield had moved from 4.20 to 4.17 per cent. A reader given only those two month-end numbers would conclude that April had been a quiet month. Inside it, the index fell 12.1 per cent over four sessions, rose 9.5 per cent in a single day, and printed annualised realised volatility of 50 per cent against 17 per cent in the two months before.

Figure 1 plots the month across three markets. The gap between what the endpoints say and what the path says is the subject of this issue.

Section 01Two kinds of risk

It helps to separate two things the word volatility runs together. Diffusive risk is the continuous, small, roughly symmetric jostling of prices that classical models describe well. Jump risk is discrete, large, of uncertain sign, and triggered by events. A scheduled policy decision is close to pure jump risk: the market often knows when the announcement will come and not what it will say, and the outcome resembles a branch rather than a drift.

Options price the two differently. Where jumps are feared, implied volatility rises, the priced distribution grows fatter tails, skew steepens because crash protection is bid, and short-dated contracts become expensive because the event is near. The theoretical home of that intuition is Merton's work on pricing options when returns can be discontinuous: admit jumps and the option price must carry a term for their size and frequency, not merely for day-to-day variance. The VIX panel in Figure 1 is that pricing in one dimension. It runs from 21.51 on 1 April to a peak of 52.33 on 8 April, then back to 24.70 by month end.

Section 02What the three panels show

The announcement came after the US cash equity close on 2 April, so the first full session to price it is 3 April. The index fell 4.84 per cent that day and 5.97 per cent the next, reaching 12.14 per cent below its 1 April level by the close on 8 April. On 9 April, after a ninety-day pause was announced for most countries, it gained 9.52 per cent in one session.

The Treasury panel is the one that resists a simple reading. The 10-year yield first fell to about 4.01 per cent, the ordinary flight-to-quality response, and then rose above 4.53 per cent over the following week while equities were still unsettled. A haven asset that sells off during a risk-off episode is a signal about the market for the haven itself rather than about the shock, and this article does not attempt to identify which of the several proposed explanations accounts for it. It is recorded because a transmission story that only shows equities and the VIX would leave it out.

A market that falls and recovers has not been calm. It has been violent twice, and a month-end snapshot cannot say so.

Section 03Volatility is path dependent

Realised volatility is built from the squares of returns along the path, so a round trip generates a great deal of it even when the endpoints nearly coincide. Between 1 February and 1 April the annualised standard deviation of daily log returns on the S&P 500 was 17.2 per cent. Between 2 April and 30 April it was 50.1 per cent, close to three times as high, while the index ended the month within two per cent of where it started.

The normalisation afterwards was equally complete. Over May and June realised volatility was 13.5 per cent, below the pre-announcement level. Whatever April did to the distribution, it did not persist in the realised path, and a reader should resist the tempting conclusion that a violent month leaves a permanently more volatile market behind it. In this episode it did not.

Attribution is where care is most needed. The window in Figure 1 contains other news, no counterfactual path exists, and an event study cannot separate the announcement's effect from everything else that happened in April. The Bank for International Settlements, reviewing the episode later, estimated that roughly three-quarters of the S&P 500's rise from the 9 April trough through the end of July reflected positive surprises unrelated to tariffs. Policy reversal helped offset the initial shock. It does not account for the recovery.

price path:   dS/S  =  mu*dt  +  sigma*dW  +  J*dN
                        (diffusion)      (jump on arrival dN)

implied vol before a known event embeds E[J^2]     # the surface, not a level
realised vol^2  ~  sum_t ( r_t^2 )                 # depends on the actual path

measured, S&P 500, annualised standard deviation of daily log returns:
    1 Feb to  1 Apr 2025    17.2%      (n = 41 sessions)
    2 Apr to 30 Apr 2025    50.1%      (n = 20)
    1 May to 30 Jun 2025    13.5%      (n = 41)

index level, 30 April versus 1 April:  -1.80%

The episode separates three objects that a single word usually collapses. Before the announcement, option prices represented a distribution over possible jumps. During the repricing, liquidity and hedging determined the path taken through those states. Afterwards, realised volatility recorded every move even though the index had largely recovered. Policy uncertainty is a dated distribution, a transmission process, and a realised sequence, and a volatility level reports only the first of the three.

This research is analysis and commentary for general information. It is not investment advice, an offer, or a solicitation, and it contains no price forecasts. Returns and volatilities in the text are the author's own calculations from the sources cited.