Risk Measures Across Equities, Fixed Income, Commodities, and FX

# A comprehensive list of risk measures for different asset classes


# A comprehensive list of risk measures for different asset classes












Is there any list of risk measures commonly used in Equity, FI, FX, Commodities portfolio management? For instance:

Equities - standard deviation, beta; Bonds - duration, convexity, DV01; FX/Commodities - ???;

What risk measures would you look at if you were managing Equity portfolio? What if you are dealing with FI? Or FX?

Or should you just ignore these measures and monitor VaR?

## Answer by Chris Taylor (score 4, accepted)

https://quant.stackexchange.com/a/30645

VaR has the benefit that it is comparable across all asset classes, and can even be computed for multi-asset class portfolios. The downsides are that it either needs assumptions on the joint distribution of all assets in the portfolio (which is difficult to calibrate) or historical simulation/bootstrapping (which may not be relevant to the state of the market today).

For individual asset classes, some common measures of risk include

Equities

- Net book size (total longs - total shorts)

- Gross book size (total longs + total shorts)

- Standard deviation

- Beta

- Country exposures/betas

- Sector exposures/betas

- Factor exposures/betas (e.g. using BARRA or some other provider to get exposure to value, momentum etc)

- Value at risk

Fixed Income

- Net duration (sum of positions x duration)

- Gross duration (sum of |positions| x duration)

- DV01, PV01

- Country risk / duration / DV01

- Credit risk (sovereign / investment grade / high yield)

- Value at risk

Commodities

- Net book size (sum of notionals on futures and spot positions)

- Gross book size (total longs + total shorts)

- Beta to commodity index (GSCI, DJCI, BCOM)

- Sector risk / betas (e.g. energy, agriculture, precious metals, ...)

- Value at risk

FX

- Net risk vs quote currency (typically USD, but you can use any currency)

- Gross risk vs quote currency

- Country / regional exposure

- G10 and emerging market exposure

- Commodity exposure (e.g. large positions in CAD, AUD, NOK, RUB, BRL...)

- Value at risk

You can also define various custom risk measures, for example - compute the adjustment required so that the position has the same volatility as global equities - for bonds, this will mean multiplying the position by a number less than 1, for energy commodities this generally means multiplying by a number greater than 1. This allows you to compare all instruments on the same scale.

## Answer by rrg (score 1)

https://quant.stackexchange.com/a/30676

Risk measures:

- Volatility, the broadest classification regards price variance. Across asset classes the volatility of equity broadly equates to DV10 for credit/coupon instruments.

- Mean variance, Markowitz (1952) showed that if risk is measured by the variance of returns and expected return by the mean of returns, then uncertain investments can be ordered by their ranking in MV space.

- VaR, value at risk, if X is the underlying price of a portfolio, then VaR(X){\displaystyle \operatorname {VaR} _{\alpha }(X)} is the negative of the α\alpha -quantile. It estimates how much a set of investments might lose, given normal market conditions, in a set time period such as one day with α=95/99% confidence. Assumption issues are normally distributed returns, or, a concave investor utility function; it does not measure the distribution or extent of risk in the tail, but only provides an estimate of a particular point in the distribution.

- Semi variance, the SV concentrates on the returns below the mean (expected return) thus the normality assumption is not required.

- Expected Shortfall, or conditional VaR/expected tail loss, conservatively estimates the value (or risk) of an investment by focusing on less profitable outcomes. For high values of q it ignores the most profitable but unlikely possibilities, while for small values of q it focuses on the worst losses

- Lower Partial Moments, Bawa (1975) and Bawa and Lindenberg (1977) generalised this idea by suggesting models based on LPM over n orders (see for example, Sing and Ong, 2000). LPMs of order 2 are measures of portfolio risk that focus on returns below some target level, so that for example, the semi-variance is just a special case LPM.

- Min-Max, Young (1998) said given an historic time series of returns, the optimum portfolio under the MM rule is defined as that which would minimise the maximum loss over all past periods, subject to a restriction that some minimum average return is achieved across the observed time periods.

- Mean Absolute Deviation, all these measures of risk are sensitive to outliers in the data because the mean differences are squared. Here a measure of variability that is less sensitive to outliers, (Konno, 1989), equivalent to MV under normality.

There are other types of risk that you may additionally consider outside of price risk:

- Liquidity risk, defined under Basel III as LCR or NSFR.

- Operational, other non instrument factors.

- Systemic, contagion risk.

- Market risk, the expected price is absent.

Traditionally, the measure of risk used in portfolio optimisation models is the variance.

Sources:

http://centaur.reading.ac.uk/21493/1/0304.pdf http://laurent.jeanpaul.free.fr/Pres%20papierEVRY3.pdf