Managing Risk with Options and Delta Hedging

Holding a portfolio of risky investments involves three tasks: hedging, rebalancing, and monitoring. Derivatives let you manage a portfolio's alpha (skill) and its systematic risk (beta) independently. Binomial pricing and option sensitivities give you the tools to hedge directional risk and speculate on volatility instead.

Separating alpha and beta. Alpha can be sought independently of beta. Your investment staff can pursue alpha from products that offer the best opportunities, even outside the benchmark and traditional asset classes. Alternative assets fit this flexible model well. You seek beta through products that cheaply deliver market risk premiums. You can hold a portfolio that maximizes alpha while controlling its systematic risk through financial derivatives. Separating alpha and beta means managing a portfolio's alpha and its beta exposure independently toward desired levels.

Hedging systematic risk. Derivatives can alter a portfolio's characteristics without redeeming illiquid fund allocations. Suppose a diversified portfolio has equity beta ${\beta }_{Port}$. You reduce that beta by selling equity futures (a short position).

Common mistakes

• Treating delta-hedging as a directional bet. Delta-hedging eliminates directional risk, so the combined position generates roughly zero profit from price moves. If you think a stock is mispriced, just buy or short it. Delta-hedging is a speculation on volatility and on a derivative being mispriced relative to its underlying.
• Believing the stock trades generate the profit. If a stock is informationally efficient, all trading strategies on it have an NPV of zero. Convertible-arbitrage commentaries that attribute expected profit to the hedging stock trades are wrong when the stock is efficiently priced. Trap: a question implies the stock leg earns the alpha.
• Using the wrong put delta. Put delta is $N(d_1)-1$, not $N(d_1)$. If $N(d_1)=0.55$, the put delta is −0.45, not 0.55. Remember that call and put deltas have opposite signs and always differ by 1.

Bottom line

• Hedge systematic risk with ${\beta }_{New}={\beta }_{Port}+(F/P){\beta }_{Futures}$, where ${\beta }_{Futures}\approx 1$ for a broad index futures contract.
• Portable alpha ports a strategy's alpha onto a target beta using two futures: short the native beta and go long the benchmark beta.
• Put-call parity is $+\text{Stock}+\text{Put}-\text{Call}=+\text{Bond}$; the hedged combination equals a riskless zero-coupon bond with face value equal to the strike.
• Call delta is $N(d_1)$ and put delta is $N(d_1)-1$; the two differ by 1 with opposite signs, while calls and puts share gamma and vega.

Exam shortcut

Read the stem for the goal first: change beta, price an option, or harvest a rebalancing return. Then apply the right tool. DECISION: To change beta, solve ${\beta }_{New}={\beta }_{Port}+(F/P){\beta }_{Futures}$ for $F$. A positive $F$ means go long futures (raise beta); a negative $F$ means go short futures (lower beta).

The full lesson (about 3,525 words, 24 min read) adds 2 worked examples, all 7 common mistakes, a self-check, free in the app.

Learning objectives

• alpha systematic risk
• portfolio options
• delta hedging
• delta hedging observations
• mean reversion diversification
• hierarchy alpha
• types alpha
• risk premia betas
• manufactured alpha evidence
• benchmarking attribution overview
• single factor benchmarking
• multifactor benchmarking
• alt asset benchmarking
• benchmarking commodities
• benchmarking managed futures
• benchmarking pe
• peer group benchmarks
• benchmarking re
• margin collateral
• var managed futures
• other liquidity methods
• smoothed returns
• modeling smoothing
• unsmoothing hypothetical
• unsmoothing re data
• risk measurement overview
• risk aggregation
• info categories
• data freq daily weekly monthly
• data freq quarterly annual
• cybersecurity
• risk mgmt structure process

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