# How Much Risk is in My Portfolio?

**Measuring risk** is the first step in **controlling risk**. In a diversified portfolio, most risk is **systematic risk**, since a lot of the non-systematic risk is diversified away. Systematic risk is explained by one or more **risk factors** such as stock market risk or interest rate risk. My research suggests that **four risk factors** will capture most of the risk in most portfolios.

__What is Risk?__

For most investors, **risk is not having the money you need when you need it.** To equate risk with **volatility** is by this definition a gross over-simplification. For one thing, risk only has to do with **downside volatility**. No one complains about upside volatility!

Some people would call risk **a permanent impairment of capital**—a
loss that you do not have time to make up for by changing your spending
habits or plans for working or not working. Your ability to make these
kinds of changes is the main reason why your investment time horizon
matters.

**You should not assume that holding on for the long-term will get you a return like the average from the past. **That
is, based upon what has happened in the U.S. stock market over some
lengthy historical time period, you may believe that if you just ride
out the short-term volatility, your long-term return will converge
toward the historical average.

Granted, it is a statistical truth that future returns will vary around the future average (mean) return. The problem is that **no one knows what the future average return will be!**
U.S. stock market returns have been the best in the world, by far, over
the long-term. Not everyone has been so lucky. Think of Russian
investors in 1918, German investors in 1945, or Cuban investors in
1958. Not all of the bad outcomes have to do with wars or revolutions
either. Japanese investors have waited decades to recoup their losses.

The future is uncertain. **Risk control matters.**

__Volatility as Risk__

If returns are “**normally distributed**” (fall along a bell-shaped curve), then returns will be **symmetrical**,
so that downside deviations from the mean are expected to be the same
size as upside deviations from the mean. (Investing in instruments that
truncate the payoffs, such as options, would invalidate this
assumption.) This greatly simplifies calculations and allows the use of
**“parametric” statistical tools**, such as **regression analysis**, t-tests for distributions, etc. Using the **standard deviation as a measure of volatility** is valid under this assumption.

Actual returns of U.S. stocks are not quite normally distributed. For one thing, returns are closer to **log-normal **(shown
in the graph above), but even that is not quite enough of a
transformation to cure the non-normality. The most glaring statistical
problem is the “**fat tails,**” especially the **large negative returns**
that come up more often than predicted by parametric statistics. The
orange bars in the graph count the number of months that fall into 40
different “z-score bins.” The z-score bins group monthly returns by
standard deviations above or below the average. The lowest bin was for
October 1987’s return of -21.76% which was 5.7 standard deviations below
the mean. The probability of a -5.7 standard deviation event occurring
is extremely remote—something like once every 720,000 years! Despite
these left tail outliers, most observations fall roughly along a
log-normal distribution, so most analysts go ahead and use parametric
statistical tools to analyze stock returns but keep in mind the
heightened possibility of extreme left tail events.

__% in Stocks vs % in Bonds is Not Enough__

**The overwhelming majority of risk in most portfolios is stock market risk**—something
like 80%-90% in most cases. Measuring and controlling stock market
risk is the most important task of a portfolio risk management system.
However, many investors have **only a very rough idea** of how much stock market risk they have based on how much they have allocated to **stock funds compared to bond funds**.
That is, if they have 60% allocated to stock funds, they assume that
they have 60% of the risk of the stock market. This is a faulty
assumption.

**Not all stock funds have 100% of the risk of the stock market**. Some have more, some less. The usual way to measure how much stock market risk a fund has is to **regress the fund’s returns against the returns of a benchmark**
stock market index like the S&P 500. Another (slightly more
accurate) method is to regress the returns of the fund’s individual
stock holdings against an index and aggregate the results. The result
is a “beta” from the regression formula:

R_{p} = a + bR_{m} + e

Where:

R_{p} = portfolio return (or R_{s} for stock return)

a = “alpha” average return regardless of the market’s return

b = **“beta” or sensitivity** of the portfolio’s return to the market’s return

R_{m} = return of the market

e = unexplained return or “error”

The classic calculation of stock market beta uses the most recent 60 months of equally-weighted returns. I prefer to use **36 months of returns**, and **exponentially-weight**
them so that the most recent 12 months have half of the weight. I find
that this methodology is more forward-looking and therefore more
accurate.

**Most stock funds** will have a market beta of **close to 1.00**, but low volatility funds will have a lower beta. For example, my risk model estimates that the market beta of the **iShares MSCI Min Vol ETF (USMV)** is **.78**. Some funds have a beta above 1.00. Often technology funds will have a high beta. For example**, iShares PHLX Semiconductor ETF (SOXX)** has a market beta of **1.33** according to my risk model.

**You can’t assume that all stock funds have a beta of 1.00. And you can’t assume that all bond funds have a beta of zero.**
Most bond funds have some sensitivity to the stock market because
corporate bonds are exposed to some of the same risk factors that drive
stock returns, especially credit risk. For example, **Vanguard Total Corporate Bond ETF (VTC)** as a stock market sensitivity of **.09.** As you might expect, high yield bonds have a much greater sensitivity to the stock market. **SPDR Bloomberg Barclays High Yield ETF (JNK)** has a stock market beta of **.26** in my risk model. Convertible bond funds have an even higher level of stock market risk. **SPDR Bloomberg Barclays Convertible Bond ETF (CWB)** has a market beta of **.77**. This bond fund has as much stock market risk as some stock funds!

__The Four Risk Factors__

Stock market risk is the most important risk factor for stock funds. **For bond funds, the most important risk factor is interest rate risk.** For example, **Vanguard Total Bond Market ETF (BND)** has a sensitivity to changes in the **10-Year Treasury Bond Index** of **.59**. International funds, whether stock or bond funds, add currency risk to the picture. For example, **Vanguard FTSE Developed Markets ETF (VEA) **has a sensitivity to changes in the **U.S. Dollar Index** of **-.74**.
Broad commodity funds (those that invest in many different commodities)
tend to have a high sensitivity to oil prices. For example, **iPath S&P GSCI Total Return ETN (GSP)** has a sensitivity to changes in **oil prices** of **.58**.

My research has found that **four broad risk factors will capture most of the risk in any fund:**

**Stock market risk (MKT)**, as measured by the**S&P 500 Index****Interest rate risk (LTB)**, as measured by the**10-Year Treasury Benchmark Index****Currency risk (DLR)**, as measured by the**U.S. Dollar Index****Commodity risk (OIL)**, as measured by the**West Texas Intermediate Crude Oil Index**

It is very important to **measure the sensitivity** **of each fund to these four risk factors** **simultaneously, using multiple regression analysis** that includes all four risk factors. It is also very important to use **exponentially-weighted**
multiple regression analysis. The exponential weighting helps make the
calculations more sensitive to changes, and thus more forward-looking.

__Predicting Future Volatility __

The point of measuring the sensitivities to the four risk factors is to construct portfolios that have low **downside volatility**.
The fund’s contribution to portfolio risk depends not only on how
sensitive the fund is to the risk factor but also on how volatile that
risk factor is. **Factor volatility** tends to follow a
well-documented pattern—during normal times it bounces around its
historic average range but during times of stress it **spikes upward and then diminishes back down**
towards the norm over time. (See graph below.) Factor volatility does
not spike downward, only upward. This pattern means that next month’s
factor volatility (as measured by 30-day standard deviation of return)
will tend to be highly correlated to this month’s factor volatility.

Thus, the best forecast for next month’s factor volatility is between this month’s factor volatility and the longer-term average volatility. However, the current volatility environment matters a lot. Here are the monthly serial correlations of the 30-day daily volatility for the four risk factors since 1990:

- MKT 74%
- LTB 51%
- DLR 57%
- OIL 61%

There are **extremely high month-to-month correlations**.
When risk for a factor spikes up, that elevated risk level is apt to
last for a while. It is also worth noting that for stock market risk,
future returns tend to be inversely related to volatility. That is,
when stock market volatility is high, stock returns tend to be lower
than average. Therefore, modestly lowering stock market risk when
stock market volatility spikes up will help control risk and may also
slightly enhance return, if historical patterns continue to hold.

__Conclusions__

- Returns are highly variable and future average returns are unknown.
- Return volatility is a reasonable way to measure risk.
- Stock market risk is by far the largest risk in most portfolios.
- The percentage allocated to stock funds is an inaccurate estimate of stock market risk.
- Stock market “beta” is a statistical way of measuring stock market sensitivity.
- The stock market betas for stock funds vary widely.
- Most bond funds also have some stock market sensitivity.
- Other important risks include interest rate risk, currency risk, and oil price risk.
- How much risk a fund adds to a portfolio depend upon both the fund’s sensitivities to the risk factors and the volatilities of those risk factors.
- Risk factor volatilities can spike up suddenly.
- Because periods of high volatility tend to lead to further high volatility, it is prudent to trim back on factor exposure when factor volatility spikes up.

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