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# Don’t Choose Between Rain or Sun – Pick Both

November 29, 2011 | Daily Capital

Correlation, as scary as it sounds, can be a key source of both lowering your portfolio’s risk and increasing your return. It merely defines how one security tends to move in relation to another, and to better understand and illustrate its magic, let’s step into a simple, imaginary world, then we’ll look at how these imaginary examples translate in to the real world to both boost returns and lower risk.

Imagine that you live in a simple world where a year is either sunny or rainy, nothing in between. There is a 50 percent chance for either and the weather forecasters have a dismal track record. Now imagine that you are considering buying stock in two different companies: Rainy Day Umbrellas, Inc. which sells millions of umbrellas in rainy years but its sales force starves in sunny years, or Golden Tan, Inc., which sells millions of sun care products in sunny years but products just sit on the shelf in rainy years.

Now imagine that you have \$10,000 and each stock is selling for \$50 a share and will have the following up and down sides:

[table id=7 /]

In deciding whether you pick Rainy Day Umbrellas or Golden Tan, your expected return will be 10 percent, the mid-point of the +30% and -10%. By buying half of each, you also have a 10 percent expected return but you eliminate all volatility as follows:

[table id=8 /]

What you have done is eliminate risk. You get the same \$1,000 or 10% gain no matter what the year holds.

# Increasing Return

Now it may not look as though you’ve increased return since you would have expected to make that same 10% return no matter which stock you picked. The magic however begins in the second year. You rebalance and put half of the \$11,000 in each stock and have the following results in the second year:

[table id=9 /]

In a two year period, you earned 10% annually and your portfolio is now worth as follows: \$10,000 x (1+10%)2 = \$12,100. On the other hand, if you bet on one company each year, the odds are that you’d be right on year and wrong on one. The math works out as follows:

• Right on year 1: \$10,000 x (1+30%)*(1-10%) = \$11,700
• Right on year 2: \$10,000 x (1-10%)*(1+30%) = \$11,700

So you end up with \$400 less (\$12,100 – \$11,700) by betting on one company, not to mention a lot more risk.

# The Real Benefit of Being Bad

In this fictitious world, the two stocks had a perfectly negative correlation of -1.0 which is being as bad as one can be. A perfectly good correlation of +1.0 would have provided no benefit at all. In the real world, other than Treasury bonds, we can only find investments that have lower positive correlations to stocks. Nonetheless the same benefits still exist, though they can only lower risk rather than eliminate it.

Holding a high quality bond portfolio and rebalancing can provide a bit of the benefits from negative correlations. Also, alternative asset classes like Real Estate Investment Trusts (REITs) and precious metals and mining have lower positive correlations and disciplined holdings can smooth out the total portfolio volatility. Most investors, however, will by these alternative asset classes to performance chase rather than diversify.

Don’t just buy negative correlations at any cost. Options and hedge funds can have negative correlation but at a cost that’s far too high in my book. Also, even securities like bonds with negative correlations to stocks can move in the same direction as they did in the stagflation years in the 70s.

Buying asset classes with lower correlation isn’t the magic bullet of earning high returns with little risk. If used correctly, however, it can both lower risk a bit and give you a bit of a higher return.