## Saturday, August 8, 2015

### The Arithmetic of Loss

 Rubik's Cube

If you played King of the Hill as a child, you'll remember the goal was to beat the other kids to the top. Not easy (at least it wasn't for me). But going down the hill was a breeze. The other kids and gravity were always ready to help!

It's easier to go down than up - this is the world of physics. The principle for how this applies to investments is called the Arithmetic of Loss.

The math: losses hurt more than gains help. For example, losing 5% is more negative than gaining 5% is positive.

Shouldn't the effect be equal? We'd think gaining 5% or losing 5% would have the same impact. But no.

To illustrate, consider a bigger percentage. Start with \$100,000 and gain 50%, and you're \$150,000. Great.

But as we know from the law risk equals potential return, where there's a chance for return, there's one for loss. Suppose the sword cuts the other way and you lose 50%. You'd have \$50,000. Here's the rub: to get back to \$100,000, you now have to go up 100%.

One more example: an investment of \$100,000 earns 10% a year for three years. In the fourth year, it loses 10%. The ending value is \$119,000. This computes to a return of just 4.6% per year. One down year disproportionately reduced the result.

#### You Can Only Lose All Your Money Once

 Las Vegas in the 1950s

There is another important aspect to the arithmetic of loss. Gamblers in Vegas know
this - your capital is finite. Once it's all gone, it's gone.

When you lose, you may become more risk averse. Math is compounded by psychology - studies show losses hurt more emotionally as well. With capital depleted, you'll likely be less tolerant of further losses.

#### Risk Tolerance May Change with Market Conditions

Consider an investor who retires with what they figure is twice what they need to live comfortably. They take some risk. But if they suffer big losses, they will rethink their risk tolerance. They'll probably become more conservative and move what's left to safer instruments.
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 Daily Linear Chart of S&P 500 from 1950 to 2013

When do investors lose money? During a market decline. Reallocating a portfolio to reduce risk during a market decline means selling the riskier assets in a down market, which is often bad timing.

#### Does Buy and Hold Protect Against Losses?

In the past, it was believed a buy and hold strategy would protect against losses. The value of an investment may temporarily decline, but the solution was easy: don’t sell. Just hold until the value came back.

This approach was based on the idea that the market and investments will always quickly go up after a decline. The problem is, that may not always be the case, especially during a shorter time frame. A better strategy is to accurately assess risk tolerance in advance.

Mathematically, just like in King of the Hill, it's much easier to go down than up. I don't know why it has to be this way. But kids -  and investors - have to live with it.