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Judge the approaches available for reducing volatility risk within a portfolio and outline the difficulties of managing that risk.

FRM® Part II · Risk Management and Investment Management · Factors · FRM2.IM.2.c

The idea

Volatility risk is the risk that market volatility rises, which usually coincides with falling prices. Investors can reduce it in four ways. They can hold less equity and more bonds or cash. They can buy protection through index puts, variance swaps or volatility futures. Protection is costly because implied volatility exceeds realized volatility on average, so insurance earns a negative expected premium. They can tilt to low-volatility stocks. Or they can follow rules that cut risk when volatility rises, such as volatility targeting, where target is the volatility the investor wants and forecast is the forecast volatility of the risky asset: Weight = target ÷ forecast. The difficulties are several. Volatility is persistent but mean-reverting and jumps, so rules react after losses and can sell low and rebuy high. Trading costs apply. Selling volatility to earn the premium adds crash risk exactly in bad times. Every hedge costs expected return, and no approach is free.

Formulas

Risky weight under volatility targeting

w = σtarget ÷ σforecast

σtarget
the portfolio's target volatility
σforecast
the forecast volatility of the risky asset

Treats the rest as riskless cash. If the rest is bonds with their own volatility and correlation, the full two-asset variance must be solved instead, which gives a different weight.

A practice question

From the question bank, with the reason each wrong option is wrong.

Why is protection against rising volatility, for example through index options, typically expensive for a long-term investor?

  1. Index options cannot be traded in size, so hedges must be built from illiquid assets.Why not: The cost is a negative expected premium, not an inability to trade; index options are liquid.
  2. Volatility spikes when equities fall, so protection pays off in bad times and carries a negative expected excess return. - correct
  3. Volatility cannot be forecast, so any hedge has zero expected cost.Why not: Confuses unpredictability with zero cost; hedges still carry a negative average premium.
  4. Volatility is positively correlated with equity returns, so the hedge pays off when investors are already doing well.Why not: Reverses the sign: volatility rises when equities fall, so the correlation is negative.

Because volatility protection pays off in bad times, it is a hedge. Investors bid for hedges, so implied volatility tends to exceed realized volatility and protection costs expected return.

A harder one

A portfolio targets 10 percent volatility by holding equities and cash. Equity volatility was forecast at 12.5 percent and is now forecast at 20 percent. Ignoring costs, by how many percentage points of portfolio value should the equity weight be reduced?

  1. 37.5 percentage pointsWhy not: Expresses the cut as a fraction of the old position (30/80) instead of points of portfolio value.
  2. 50 percentage pointsWhy not: Reports the new equity weight as if it were the reduction.
  3. 30 percentage points - correct
  4. 7.5 percentage pointsWhy not: Uses the change in forecast volatility (20 - 12.5) rather than the change in the target weight.

Weight = target / forecast volatility. Before: 10/12.5 = 80%. Now: 10/20 = 50%. Reduction = 80% - 50% = 30 percentage points of portfolio value.

The hardest tier

A risk manager uses volatility targeting, cutting equity exposure when forecast volatility rises. Which statement best judges its usefulness and limits?

  1. It eliminates drawdown risk, because exposure is always scaled to the target volatility and so cannot produce large losses.Why not: Weights are scaled to forecast, not realized, volatility; jumps and gaps still cause losses.
  2. Volatility is persistent, so it is forecastable, but jumps hit before exposure is cut and reversals cause selling low and rebuying high. - correct
  3. It works only if volatility is constant, so it fails whenever volatility clusters.Why not: Reverses the logic: volatility clustering is what makes recent volatility a useful forecast.
  4. Its only cost is the lost equity premium, since trading between equities and cash is costless and cannot whipsaw the portfolio.Why not: Ignores trading costs and whipsaw when volatility spikes and quickly falls back.

Volatility clustering makes targeting partly effective, but jumps arrive without warning, mean reversion can cause sell-low/buy-high whipsaw and trading costs reduce the benefit.

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