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By Brad Zigler

The recent rebound in gold prices, coupled with a buoyant (well, until this week, anyway) equity market, prompted many investors to wonder if their fortunes would be better hitched to mining stocks than bullion. Based on the performance of large gold producers over the past three months, the answer's an unqualified "maybe."

A little explanation's in order.

The universe of gold producers is fairly well represented by the 30-issue index tracked by the Market Vectors Gold Miners ETF (GDX). Over the last three months, the index remained virtually unchanged, while gold appreciated 2.3 percent. Gold producer share prices, collectively, didn't keep pace with bullion — a fact that shouldn't surprise anyone who knows the correlation between gold prices and the GDX index is currently 82 percent.

While it looks as though gold stocks displayed only some of gold's price volatility, miners were actually more voluble. Gold stocks rose faster than bullion late last year, only to fall harder when gold prices slumped:

Market Vectors GDX Vs. Gold

Market Vectors GDX Vs. Gold

Not every issue in the GDX portfolio followed this track, however. In fact, seven of GDX's 10 largest constituent stocks produced gains for the period, though some looked pretty ugly doing so. Those top 10 issues make up nearly three-quarters of the index market weight.

These issues aren't as highly correlated to gold as the whole index is; the average coefficient for the 10 weighty issues is only 66 percent. For some of these stocks, the weaker correlation stems from outsized performance. Take Yamana Gold, Inc. (AUY), for instance. Yamana rose nearly 10 percent since November, but was twice as volatile, day to day, as bullion.

Day-to-day volatility is tracked by taking the standard deviation of an asset's daily returns. Yamana's annualized volatility for the past three months is 27.1 percent. Bullion's is 14.4 percent.

More commonly, a stock's relative volatility is usually advertised as its beta. Beta is a comparative metric that casts a stock's return against that of an equity benchmark such as the S&P 500 Composite. A stock with a beta of 1.00 is just as volatile as the benchmark. Higher betas — that is, readings of 1.01 and greater — reflect higher volatility; values at 0.99 or less denote slower-moving issues.

For gold stocks, you can use gold as the bogey instead of the S&P. Measured against the metal's returns, the GDX heavyweights average a 1.39 beta. You could say that these stocks, on average, are 39 percent more volatile than bullion.

Three-Month Performance (23-Nov-10 Through 23-Feb-11)

Weight

in GDX

Period

for Return

Correlation

to Gold

Beta

vs. Gold

Alpha

vs. Gold

Barrick Gold (ABX)

17.0%

3.4%

.75

1.33

.02

Goldcorp (GG)

11.1%

0.9%

.70

1.18

-.07

Newmont (NEM)

9.5%

-2.4%

.70

1.16

-.20

Anglo Ashanti (AU)

6.1%

3.5%

.64

1.17

.03

Kinross Gold (KGC)

5.8%

-11.8%

.55

1.17

-.50

Silver Wheaton (SLW)

4.8%

15.2%

.75

2.51

.53

Yamana Gold (AUY)

4.6%

9.6%

.72

1.34

.32

Gold Fields (GFI)

4.5%

5.6%

.64

1.20

.13

Co. Buenaventura (BVN)

4.4%

-15.5%

.49

1.34

-.62

El Dorado Gold (EGO)

4.4%

0.2%

.69

1.46

-.13

Sometimes, that extra volatility pays off in a market-beating return. That's best measured by alpha. Alpha tells you how much better (or worse) the stock is doing against its beta-adjusted market return. Positive alpha is good, negative is bad.

Yamana's 9.6 percent gain, when extrapolated over a year's time, is 32 percent better than its beta projects, while Goldcorp's (GG) negative alpha tells you that its current return, projected over a year, is 7 percent worse than you'd expect, given its beta.

Essentially, alpha tells you how much payback you get for taking the stock's volatility aboard. Keeping tabs on alpha also allows you to quickly zero in on issues at the extremes in your portfolio. Why, for example, did Silver Wheaton Corp. (SLW) jump so much more than its peers? (Hint: The answer's found in the firm's name). Or are shares of Compania de Minas Buenaventura (BVN), thoroughly beaten up in the last quarter, now due for a rebound?

To get to alpha, you first have to go through beta. With an Excel spreadsheet, you can calculate beta with the argument:

= COVAR(stock returns, market returns)/VAR(market returns)

Then, with beta in hand, alpha can be determined as:

= (stock return - risk-free return) - beta * (market return - risk-free return)

Thus, with a just few keystrokes, you should be able to see which of your stocks is the alpha dog as well as identifying those that need to be unhitched.

Source: How's YOUR Gold Miner Doing?