dollar beta is $25.5m. SPY has a beta of 1. If we sell the entire SPY position and further short $15.5M, the total beta of the portfolio is zero. The market component of the portfolio volatility is proportional to its dollar beta, and is therefore zero. And the idiosyncratic risk of the portfolio? It has not changed, because SPY has no idio volatility (to a very good approximation). The summary statistics of the hedged portfolio are in Table 3.7. The procedure is described in Procedure Box 3.2.
Table 3.7 Synchrony, Wal-Mart and SP500 risk parameters, together with holdings for each asset for a market-hedged portfolio.
| Field | SYF | WMT | SPY |
|---|---|---|---|
| Beta | 1.2 | 0.5 | 1 |
| Daily Market Vol (%) | 1.4 | ||
| Daily Idio Vol (%) | 1.2 | 0.7 | 0.0 |
| Net Market Value ($M) | 10 | 5 | −15.5 |
Procedure 3.2 Compute the market hedge of a portfolio.
1 Compute the dollar betas for the individual positions of the unhedged portfolio;
2 Compute the dollar portfolio beta as the sum of the individual betas;
3 Compute the market hedge NMV, whose value is equal to the opposite of the portfolio beta.
This is perhaps the simplest possible hedging scenario one may imagine, and yet it is applied daily to portfolios with Gross Market Values10 of hundreds of billions of dollars. These portfolios are usually long-short, but they still do carry beta exposures, which are computed and hedged several times a day using liquid instruments like equity futures. In Chapter 6 we will expand the concept in several directions.
3.7 Separation of Concerns
We saw that a simple factor model enables you to do performance attribution, risk decomposition and hedging. These three tasks are tightly connected. If from risk decomposition you can detect that market risk is large, then it is more likely that a substantial fraction of your PnL is attributable to market returns, and this also means that this market risk can be completely hedged, and that the market-originated PnL can be eliminated. Behind it all, this framework enables you to see at work a fundamental design principle: separation of concerns [Dijkstra, 1982]. Disparate activities like building a car, writing the code for a video game or managing a portfolio have one thing in common: they are tasks that require solving many problems at once. If we had to address them all at once, we would likely build a Ford Pinto,11 release Duke Nukem Forever12 or be forced to shut down in record time. In order to control complexity, we need to identify smaller, simpler parts of the system; we need to separate them and solve the issues related to them; and finally we have to put them back together with little effort. Modularization, Encapsulation, and Composition. Factor models allow us to separate factor idiosyncratic returns. In the process, they help us separate unwanted risk and performance from intentional risk and performance. When we size our positions, we do so to capture the sources of returns that are specific to a firm. We have a clean way to address the unwanted risk, via hedging. Even better: in the following chapters you will learn about factors and their interpretation, so that the subsystem that constitutes “unwanted risk” can give you context about the investing environment. And this environment can be further decomposed in smaller components, such as country, industry and style risks, which we will cover in the following chapters.
3.8 Takeaway Messages
Risk models serve four main purposes:
1 Risk Measurement: Estimate the volatility of a portfolio, and from this estimate, the probability of the loss exceeding a certain threshold.
2 Risk Decomposition: The risk comes either from common sources (systematic component) or stock-specific sources.
3 Performance Attribution: Systematic and idiosyncratic sources of returns determine also the performance, and the entire performance of a book through time can be attributed to a combination of both.
4 Hedging: Once the systematic source of risk has been identified, it can be removed without affecting the idiosyncratic sources of return (and risk).
Notes
1 1 SPY is an ETF closely tracking the SP500 index.
2 2 Actually, not that easy. See the notes at the end of this chapter for more details on this topic.
3 3 See the surveys by Gabaix [2009], Cont [2001] and references therein.
4 4 This does not mean that the average absolute size of returns is 1%; see the FAQ chapter for an explanation.
5 5 The Net Market Value, or NMV, is the signed dollar holding value of security held in a portfolio.
6 6 This definition makes sense only for assets with a non-zero portfolio NMV, and typically a positive NMV, i.e., for net-long portfolios.
7 7 If you want to understand the reason why the idiosyncratic volatility of a diversified, long-only portfolio comprised of many stock is low, you can read the next-to-last question in the Risk FAQ (Section 4.2).
8 8 The annualized tracking vol is approximately . The annualization calculation is explained later, in Section 4.2. You can ignore the details of the calculation on a first reading.
9 9 In this event, the Prime Broker usually attempts to locate new stocks before forcing covering the position.
10 10 The Gross Market Value (GMV) of a stock is the absolute value of the Net Market Value. The GMV of a portfolio is the sum of the GMVs of the individual positions.
