Traders and investors often use leverage as a crude risk measure. It's an easy way to relate to how much you're risking. If you have a portfolio worth $100,000 and you borrow to buy $150,000 worth of IBM, you've 1.5 times leverage. As simple and intuitive that this approach is, it's also dangerous and can lead to flawed investment decisions.

## Even professionals make this mistake

Ok, so you made up your mind to buy Apple (NASDAQ:AAPL). How much are you going to buy? How do you decide? Surprisingly many people, even professional asset managers, will tell you that they have a default exposure. They might have a rule where they normally take a 5% position for instance. With 5% position sizes, you can buy 20 stocks before you run out of cash so it makes for a reasonable portfolio approach, one might think. If the asset manager sees a stock as a little more risky or if he has less conviction, he might take a half unit of 2.5% instead. That's how surprisingly many people approach position sizes and the risk that's implied by it.

You'll notice the same mentality on market television. A commentator might remark that a hedge fund was 10 times leveraged, implying that they were taking crazy amounts of risk. The reality is that this number really doesn't mean anything. Having a 10 times leverage might be high risk, but it might also be a low risk. The leverage alone is not enough to indicate anything about risk.

## Leverage does not equal risk

Leverage tells you how much notional exposure you have in relation to your total capital. You buy $120,000 worth of GOOG on a $100,000 portfolio, buying on margin. You would then have a 1.2 times leverage and a 120% exposure to Google. If you trade futures, it's even easier to take on larger exposure since you only need a small amount of initial margin. The mini S&P futures, SP, requires a margin of around $5,000 per contract. On the same $100,000 account, you could buy 20 of those for a total exposure of around #1,840,000 and thereby a leverage of 18 times.

Naturally, buying almost two million worth of the S&P 500 index on a $100,000 portfolio is quite risky. You could also say that it's twice as risky to buy 20 contracts compared to buying 10. So far the leverage logic holds up. But as soon as you introduce more than one asset, it breaks down fast.

## Single asset class scenario

Let's look at a single asset portfolio first. Even for a portfolio of just stocks, you can see the problem. The stock portfolio in the table below is created to illustrate the effect. The stocks themselves are randomly selected and the prices are not current. This is to demo an effect, and constitutes no recommendation for or against any of the portfolio holdings.

There are 20 stocks in total and they've all been allocated an exposure of 5%, for a total of 100% exposure on this one million dollar portfolio. There is therefore no leverage employed. This is a common way to construct a portfolio.

The Average True Range Percent (ATR%) column is a measurement of how much each stock normally moves on an average day. It's a common estimator of expected daily price variation, and though simpler it will give a very similar result to standard deviation or other common methods. The column Expected Dollar Move tells you how many dollars will on average be gained or lost per day for each position, assuming that volatility doesn't change.

Ticker | Price | Portfolio Weight | Dollar Amount | ATR% | Expected Daily Dollar Move |

AAPL | 434.77 | 5% | 50,000 | 3.22% | 1,611 |

ADM | 33.9 | 5% | 50,000 | 1.45% | 727 |

AZO | 399.63 | 5% | 50,000 | 1.62% | 811 |

BIIB | 197.51 | 5% | 50,000 | 1.62% | 808 |

COG | 66.34 | 5% | 50,000 | 2.12% | 1,058 |

EL | 65.18 | 5% | 50,000 | 1.71% | 856 |

GME | 30.2 | 5% | 50,000 | 2.92% | 1,461 |

HSY | 86.35 | 5% | 50,000 | 1.05% | 523 |

IBM | 213.34 | 5% | 50,000 | 1.15% | 576 |

LIFE | 65.54 | 5% | 50,000 | 2.08% | 1,038 |

MA | 538.96 | 5% | 50,000 | 1.49% | 743 |

MHP | 51.94 | 5% | 50,000 | 2.27% | 1,134 |

MMM | 106.625 | 5% | 50,000 | 1.11% | 556 |

NRG | 24.57 | 5% | 50,000 | 1.89% | 945 |

NWSA | 30.9 | 5% | 50,000 | 1.59% | 793 |

SWK | 79.47 | 5% | 50,000 | 1.69% | 847 |

VMED | 49.8 | 5% | 50,000 | 1.49% | 743 |

WDC | 50.8 | 5% | 50,000 | 2.40% | 1,201 |

XL | 30.82 | 5% | 50,000 | 1.36% | 679 |

XOM | 90.64 | 5% | 50,000 | 1.22% | 612 |

The obvious problem highlighted here is that this simple approach accidentally allocated risk very unevenly. The performance of such a portfolio will be driven by the volatile stocks. AAPL would have more than double actual risk than IBM. By thinking of risk in terms of exposure and leverage, the result was actually a rather random risk allocation.

## Cross asset portfolios

While the problem is significant within a single asset class, it grows to Titanic proportions when you start dealing with cross asset investment strategies. In the CTA hedge fund business we deal with futures covering all asset classes, from stock indexes and bonds to commodities, currencies and interest rates. With such strategies, the concept of leverage goes right out the window. Just consider the next table to understand why.

Name | Sector | Portfolio Weight | Dollar Amount | ATR % | Expected Daily Dollar Move |

S&P 500 | Equities | 6.25% | 62,500 | 1.060% | 663 |

Nasdaq 100 | Equities | 6.25% | 62,500 | 1.285% | 803 |

Eurodollar | STIR | 6.25% | 62,500 | 0.018% | 11 |

Fed Funds | STIR | 6.25% | 62,500 | 0.006% | 4 |

Crude Oil | Energy | 6.25% | 62,500 | 1.985% | 1,241 |

Gasoline | Energy | 6.25% | 62,500 | 2.200% | 1,375 |

Lean Hogs | Meats | 6.25% | 62,500 | 1.230% | 769 |

Live Cattle | Meats | 6.25% | 62,500 | 1.079% | 674 |

Rough Rice | Grains | 6.25% | 62,500 | 1.646% | 1,029 |

Corn | Grains | 6.25% | 62,500 | 2.346% | 1,466 |

EUR/USD | Currencies | 6.25% | 62,500 | 0.851% | 532 |

GBP/USD | Currencies | 6.25% | 62,500 | 0.694% | 434 |

US 10 Year | Bonds | 6.25% | 62,500 | 0.404% | 253 |

US 2 Year | Bonds | 6.25% | 62,500 | 0.036% | 23 |

Gold | Metals | 6.25% | 62,500 | 1.400% | 875 |

Copper | Metals | 6.25% | 62,500 | 1.800% | 1,125 |

This is a hypothetical cross asset portfolio where an equal notional dollar amount has been allocated to each position. With futures you can't take exact position sizes as with stocks, but we'll simplify that part since it has no impact on the analysis.

There are 16 positions in this portfolio so we allocate a notional exposure of $62,500 to each of them. Using the same ATR% method of estimating the daily impact from each position, the result may surprise you. While corn would on a normal day gain or lose almost $1,500, the Fed Funds futures would have an average impact of $4. Yes, that's how big a difference it makes. On an average day, the corn would be 375 times more important for your bottom line than the Fed Funds.

What you'll find is that the short-term interest rates futures (STIRs) would have almost zero actual risk in the portfolio with this kind of exposure based sizing. That's because these are markets where 0.1% in a day is a very big move. For markets like this to have a chance to contribute to the bottom line, they must be given a larger weight.

Clearly the method of allocating equal exposure is not a great idea in practice. Simply filling up with positions until you run hit 100% exposure or a certain leverage factor will result in a random risk. Let's look instead at a more realistic approach to position sizes, by allocating risk instead of capital.

The next table has the same positions as the previous table, but with different sizes. Instead of aiming for an exposure level and taking whatever risk comes with that, we've turned it around here. We aim for a certain amount of risk and let the exposure land where it may. Again, the ATR% stands in as a crude estimator of risk. Feel free to replace with other volatility measures if you so please, the principle will still work.

In this table, the target is for each position to have a daily impact of $700 on an average day. That number is picked just to arrive at the same sum of the Expected Daily Move column as in the previous table. It makes for easier comparison, that's all.

Name | Sector | Portfolio Weight | Dollar Amount | ATR % | Expected Daily Dollar Move |

S&P 500 | Equities | 6.60% | 66,038 | 1.06% | 700 |

Nasdaq 100 | Equities | 5.45% | 54,475 | 1.29% | 700 |

Eurodollar | STIR | 388.89% | 3,888,889 | 0.02% | 700 |

Fed Funds | STIR | 1166.67% | 11,666,667 | 0.01% | 700 |

Crude Oil | Energy | 3.53% | 35,264 | 1.99% | 700 |

Gasoline | Energy | 3.18% | 31,818 | 2.20% | 700 |

Lean Hogs | Meats | 5.69% | 56,911 | 1.23% | 700 |

Live Cattle | Meats | 6.49% | 64,875 | 1.08% | 700 |

Rough Rice | Grains | 4.25% | 42,527 | 1.65% | 700 |

Corn | Grains | 2.98% | 29,838 | 2.35% | 700 |

EUR/USD | Currencies | 8.23% | 82,256 | 0.85% | 700 |

GBP/USD | Currencies | 10.09% | 100,865 | 0.69% | 700 |

US 10 Year | Bonds | 17.33% | 173,267 | 0.40% | 700 |

US 2 Year | Bonds | 194.44% | 1,944,444 | 0.04% | 700 |

Gold | Metals | 5.00% | 50,000 | 1.40% | 700 |

Copper | Metals | 3.89% | 38,889 | 1.80% | 700 |

## Allocate risk, not cash

Targeting a daily impact is easy. First, use a volatility estimator to figure out how much the instrument normally moves in a day. In this case ATR% is used. The S&P showed an ATR% of 1.06%. If we allocate 66,000, the S&P futures will show a daily p&l variation of around $700 if the volatility is constant. (700 / 0.016 = 66,038)

As you see, the position sizes are dramatically different. It looks like a typo, doesn't it? Almost 400% exposure for the Eurodollar and near 1,200% for the Fed Funds. A 12 to 1 leverage on a single position, in a portfolio with plenty of other big positions.

Well, I admit to including the Fed Funds just to make the example more extreme. Still, even the Eurodollar has a 4 to 1 leverage against the portfolio. Compare the notional exposure versus the risk allocation in the graph. Now we have approximately equal risk, but the notional allocation is quite different.

The total leverage on this portfolio is 18 to 1. That's an exposure of 1,800%.

Now here is the key question.

## Which portfolio out of the three carries the most risk?

My answer would be, the first one. The one with single stocks for a total of 100% exposure, using no leverage.

Now, before you start throwing eggs in my direction, consider this. If all positions have a normal day, moving the same amount as they normally do and in the same direction, the total profits or losses will be the same for all these portfolios. For the stocks however, you both have a concentration risk in a few high volatility stocks and the much more severe problem of having all positions in a single and highly correlated asset class. All your eggs are in one basket. Stocks have a very high internal correlation, and they tend to go up and down on the same day.

The second portfolio is diversified, holding many different asset classes. The problem is that the risk is concentrated on a few of them. The third portfolio spreads risk equally on a group of asset classes with low correlation to each other.

But a single position with 12 times leverage? Doesn't that mean that we'll be wiped out if that position loses 8%? Yes, it does. But worrying about the Fed Funds dropping 8% in a day is like worrying about the S&P hitting zero tomorrow. Both could happen but it would mean end of civilization as we know it. There are more realistic scenarios to worry about.

Leverage, by itself, is pointless. As a measurement, it tells you next to nothing about your risk. Allocate risk deliberately.

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