Derivatives for portfolio risk management - Volatility manag...

Learning Outcomes

After studying this article, you will be able to identify volatility risk exposures in a portfolio, distinguish volatility management approaches using equity, index, and volatility derivatives, explain how variance swaps provide pure volatility exposure, calculate payoffs and P&L for variance swap positions, and evaluate how variance swaps and related instruments apply in practical portfolio risk management. You will also learn to recognize key exam pitfalls relating to volatility strategies and pricing.

CFA Level 3 Syllabus

For CFA Level 3, you are required to understand both the risk management motivations for volatility trading and how to structure/directly price volatility in a portfolio. This article focuses on:

• Principles of volatility risk and variance risk management in a portfolio context
• Uses of volatility derivatives, including equity options, VIX futures and options, and variance swaps
• Mechanics and payoff structure of variance swaps
• Distinction between volatility swaps, options strategies, and variance swaps for risk mitigation and speculation
• Pricing and margining issues, including P&L calculation and risks in variance swap implementation
• Common exam pitfalls concerning volatility exposures using swaps and index options

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. What is the principal difference between variance swaps and volatility swaps?
2. Suppose a manager wants to hedge a portfolio against a sudden spike in equity market volatility. Should they buy ATM index puts or enter a long position in a variance swap? Explain.
3. A one-year S&P 500 variance swap has a variance strike of 0.02 and notional $100,000. If realized variance is 0.03, what is the final cash flow for a long position?
4. Why might a variance swap provide more precise delta hedging than a portfolio of vanilla options?

Introduction

Effective risk management requires not only controlling market beta and sector exposures, but also systematically managing volatility risk. This article examines how portfolio managers use derivatives to structure, transfer, or hedge volatility exposure as a discrete risk. It explains the logic and use of variance swaps—derivatives that give direct, linear access to observed (realized) variance—and compares them with approaches using equity or index options and volatility index (VIX) futures. Thorough understanding of these strategies and potential exam pitfalls is essential for CFA Level 3 candidates.

Key Term: volatility risk
The risk to a portfolio arising from changes in the expected or realized volatility of reference assets, independent of direction of price movement.

VOLATILITY RISK IN PORTFOLIO MANAGEMENT

Volatility Exposure and Its Management

Managers increasingly treat volatility itself—distinct from price—as a targeted risk. A negative shock to markets often causes volatility to spike sharply, producing greater losses in portfolios with option-like exposures. Conversely, periods of low volatility can make portfolios vulnerable to sharp reversals and volatility "crashes".

Volatility management includes:

• Hedging losses from volatility spikes (e.g., via long volatility)
• Generating income by systematically selling volatility (short volatility)
• Targeting a specific volatility profile (as in risk parity/volatility regulated funds)
• Trading volatility outright, as a separate asset class

Key Term: variance swap
A derivative contract that pays a linear cash settlement based on the difference between realized variance and a contracted variance strike, applied to a notional amount.

Key Term: volatility swap
A derivative contract that pays based on the difference between realized volatility and a volatility strike, but with a non-linear (convex) payoff, complicating direct exposure.

VARIANCE SWAPS: STRUCTURE AND APPLICATION

Overview

Variance swaps provide a pure, linear, and direct exposure to the future realized variance (usually annualized) of an asset or index. The contract makes a single cash flow at expiry, proportional to the difference between the square of realized volatility and the strike variance agreed at inception.

Variance swap payoff:

Where:

• Realized variance is usually calculated as the average squared daily log-returns (annualized)
• The strike is set so that the contract is fair at inception (value zero)
• Payoff is positive to the buyer if actual volatility is higher than expected, negative if lower

Worked Example 1.1

A fund buys a 6-month S&P 500 variance swap with a notional of $100,000 and a variance strike of $0.015$(i.e., 15$0.025$ (i.e., realized volatility of 15.8%).

Answer:
Payoff = $100,000 \times (0.025 - 0.015) = $1,000$

Practical Uses

Variance swaps allow:

• Hedging against sudden volatility jumps (tail risk)
• Speculating on increased or decreased future volatility
• Transferring unwanted variance exposure from "short gamma" positions (e.g., from option overwriting strategies)
• Portfolio insurance alternatives

In contrast with index options or VIX futures, variance swaps match realized volatility much more closely and do not require active rebalancing or complex delta/gamma hedging.

PRICING AND MECHANICS OF VARIANCE SWAPS

P&L Calculation and Margining

To value or settle a variance swap:

• Calculate realized variance from the log-returns over the swap period, annualized (e.g., 252 trading days)
• Use the contracted variance strike, set at inception based on market-implied vol
• At expiry, the buyer receives payment proportional to difference, otherwise pays the seller

The contract is typically cash-settled, and daily marking-to-market ensures credit risk is limited.

Worked Example 1.2

A variance swap has a 12% variance strike (0.0144), $50,000 notional, and at expiry variance realized is 8% squared ($0.0064$).

Answer:
Payoff = $50,000 \times (0.0064 - 0.0144) = -$400$

Variance swaps are flexible—they can be structured for various notional exposures and durations but require counterparty credit due diligence for OTC contracts.

Comparison with Alternatives

Variance swaps:

• Track variance linearly, while option strategies (e.g. straddles) provide convex (non-linear) payoff but require periodic adjustment (dynamic hedging)
• Do not require continuous rebalancing to maintain pure volatility exposure, unlike option replicating portfolios
• Can expose holders to negative returns in calm markets (variance risk premium)

Exam Warning

For the exam, be careful not to confuse volatility swaps (linear in volatility, non-linear in variance) and variance swaps (linear in variance). Most practical exam questions focus on variance swap payoffs.

RISKS, PITFALLS, AND BEST PRACTICES

Risks and Limitations

Variance swaps have several key risks:

• Tail risk: losses if volatility collapses below the strike ("seller's risk")
• Mark-to-market P&L can be volatile if market perceived volatility changes
• "Volatility-of-volatility" risk: severe swings in variance during market events
• Model and liquidity risk: difficulty in hedging/replicating swap due to wide bid/ask, or illiquidity in stressed markets

Institutional managers often combine variance swaps with other volatility derivatives for more stable protection or income.

Worked Example 1.3

You sell a variance swap on the Euro Stoxx 50 with notional €200,000 and a variance strike of 0.013. Realized volatility is only 8%. What is the P&L?

Answer:
Realized variance = $0.0064$. Seller P&L: €200,000 × (0.0064 − 0.013) = −€1,320.

Revision Tip

Carefully read calculation conventions—variance swaps typically quote the strike in annualized variance terms (not volatility), and use squares of returns.

Summary

Variance and volatility swaps are essential tools for direct volatility risk management. Variance swaps allow a manager to gain or hedge exposure to realized variance efficiently and linearly, regardless of market direction, but expose the writer to tail risks and non-diversifiable shocks. Understanding structure, P&L calculation, and implementation risks is essential for CFA candidates and practical portfolio management.

Key Point Checklist

This article has covered the following key knowledge points:

• Differentiate volatility and variance risk and describe their role in portfolio risk management
• Explain the structure, pricing, and settlement of variance swaps
• Compare variance swaps to volatility swaps and standard delta/gamma hedges
• Identify the uses, limitations, and risks of variance swaps in portfolio risk control
• Calculate payoff/P&L and margin requirements for variance swaps

Key Terms and Concepts

• volatility risk
• variance swap
• volatility swap