An advisor recently asked me to evaluate a structured CD he was considering; the market linked CD paid a variable coupon derived by the performance of a basket of 10 stocks.

*Why are we interested?*

For this particular investment, the ** correlation** between the 10 stocks has an outsized impact on total returns; in fact, it is impossible to effectively evaluate this investment without analyzing the correlation among the securities in the basket. My goal today is to define correlation and show its effects on everything from investments to the NBA draft.

*What is Correlation?*There’s a lot of buzz among basketball fans about the upcoming 2014 draft – this year’s class is believed to be the best in years and the draft is a highly anticipated event. Generally speaking, future performance of NBA rookies is highly linked with where they are drafted. Thus if you had the chance to acquire the #1 draft pick or the #5 draft pick, you would likely pay up considerably to take the #1 pick, assuming no other available information.

The linkage between draft position and future success is mathematically described as “correlation”, a statistical measure of how two variables move together. If the two variables move in lockstep, the correlation between them is 100%. (Typically this measure is shown in decimal form, such as 1.0) For example, if every #1 NBA pick went on to be the highest performing member of the draft class, every #2 pick went on to be the 2^{nd} highest performing member of the class, and so forth, there would be 1.0 correlation between draft position and performance. (FYI, Sam Bowie and Michael Jordan illustrate that correlation of draft position and performance is not 1.0! – for the more recent generation of basketball fans: Darko Milicic vs. Carmelo Anthony).

On the other hand, if there is no linkage between two factors, we speak about 0.0 correlation. For instance, there is 0.0 correlation between a rookie’s future performance and the number of letters in his first name. 0.0 correlation means that the connection between two factors is completely random.

There is yet a third correlation relationship to discuss: if there is a negative linkage between two factors it is described as negative correlation with a maximum negative correlation of -1.0. For instance, significant injuries (whether in college or during a professional career) are negatively correlated with a player’s future career success (e.g., Greg Oden).

Of course, in practice professional scouts look for correlation among many factors (e.g., height, wingspan) that go way beyond the simple examples we use here. In addition, correlations in the real world are rarely a perfect 1.0 (perfectly correlated), 0.0 (no linkage whatsoever), or -1.0 (perfectly inversely correlated), but are shades of grey in between these numbers.

Getting back to finance and investments, correlation is a critical area to be aware of in evaluating many investments and portfolios of investments. Most investors and many products (e.g., structured notes with baskets of securities) allocate their AUM among multiple investments (i.e., a portfolio), and understanding how those individual investments move up or down together is important to predicting future performance of the overall portfolio.

Unfortunately, many investors don’t fully appreciate the impact of correlation. For example, consider the investor who splits his portfolio between ETFs tracking the S&P 500 and ETFs tracking the Dow Jones Industrial Average. He may think he is diversifying his risk, but in reality, these two indices are highly correlated (97% in 2012!). If the S&P is down in any given year, the Dow will be down around the same amount, and so the investor is achieving almost no diversification benefit because he didn’t factor in the effect of correlation.

Let’s look at the aforementioned structured CD with an eye towards the impact of correlation.

*Analyzing the product*

Since the product we were asked to evaluate was not published publicly, I am going to analyze a similarly structured CD from 2011, which will allow us to see how the product has performed over time.

Here’s the overall product design:

- 4-year note; at the end of 4 years, the original principal is returned (i.e., principal protected note)
- During each of the four years, the product pays a yield of between 0% and 5%, calculated as follows:
- The return is calculated as an average of the performance of 10 pre-selected stocks
- Each stock in the “basket” has a cap of 5% and a floor of -25% (meaning that if a stock is up 20%, for purposes of the calculation appreciation is capped at 5%, and conversely if a stock is down 40%, the loss is capped at -25%)
- Returns are “since inception”; therefore if a stock shoots up or down year 1, it’s likely to stay at the floor or ceiling until maturity of the product

Two observations immediately come to mind:

First, the methodology for calculating returns is asymmetrical and therefore skews towards providing a 0% coupon and away from providing a 5% coupon. For example, if eight stocks are up 25% and two are down 25%, return on the product for the year is 0% (8 x 5% less 2 x 25% = -10%, divided by 10, results in an average return of -1% and no coupon for the year).

Second, returns on this product are heavily influenced by the correlation of the stocks in the basket to each other. ** If all the stocks are highly correlated** (i.e. all move up or down together) annual performance results would tend towards 5% if the basket does well, or 0% if the basket is flat or down. For example, if all stocks are up 25%, then return on the product will be 5% for the year (i.e., the maximum amount obtainable). If all stocks were down 25%, then the return on the product would be 0% for the year (i.e., the minimum amount obtainable; remember, this is a principle protected note so no losses are possible). Conversely, if all the stocks in the basket were negatively correlated, the individual results would offset each other every year, and, particularly given the asymmetric return profile, would almost definitely result in a 0% return for the investor (as in the example above of 8 stocks up and 2 stocks down). Ultimately, the issuer would be best off to offer a basket of low or negatively correlated securities to minimize the required payout, while investors would desire a highly correlated basket.

Let’s do some technical analysis to figure out the actual correlation of the basket stocks and the expected performance of the investment.

Here are the 10 stocks in the basket along with their 2014 correlations:

The average correlation for the stocks in the basket against each other is 31.5%, which is considerably less than the implied S&P average of approximately 51% at the time this post was published. **Thus, the low correlation of the products in the basket puts the investor in the position of seeing coupons closer to the 0% end of the spectrum than the 5% end.**

The product launched in 2011; here’s what actual performance has been for the 10 basket stocks in the two full years since launch (note returns are cumulative since launch):

And here’s what the CD has paid, based on averaging the return of each stock in the basket, with each stock’s cumulative positive performance capped at 5% up and cumulative negative performance capped at 25% down.

As can be seen, the product paid a coupon of 0% in 2012 and 2% in 2013, despite 2013 being one of the best years for stocks on record. The product design is such that although by June 2013 9 out of 10 basket stocks were considerably up since inception, the one down stock (ABX) reduced what could have been a potential 5% coupon to 2%.

As an FYI, even in the best years of S&P performance (e.g., 2013, 2003), typically at least 10% of stocks finish down – 48 names in 2013, 42 names in 2003. So whether the issuer designs the basket with low correlation in mind or not, there is always a strong probability of at least one rotten apple in this basket, which will have the effect of spoiling the bunch and making that maximum 5% coupon highly elusive.

As an experiment, we ran a Monte Carlo simulation of expected year 1 returns if the product were to launch today. Here is the output we generated:

- The first row illustrates different potential year 1 basket returns (i.e., the actual performance for the basket of stocks, not capped)
- The second row illustrates what the expected structured product CD return would be in that basket return scenario; answers must range between 0% and 5%
- The third row illustrates how likely that potential basket return and associated product return are to occur

The weighted average of these returns and the scenario likelihoods results in an expected first year yield of about 0.38% (Note, this simulation was done recently as opposed to in 2011 and therefore correlation levels and volatility are not the same; the expected value in 2011 may have been higher). In comparison, a 4 year fixed CD would pay an estimated annual 1.90% yield, which leads to the overarching question: what would motivate an investor to purchase this security instead of a conventional CD?

In conclusion, with interest rates low, structured CDs have become more popular as investors search for alternative ways to increase yields. Sometimes, the investment leads to passing on a low but certain yield (e.g., a fixed 4 year CD) in order to receive a higher, albeit less certain yield through tying the payout to a separate security or securities, e.g., the structured CD we just analyzed.

While I continue to firmly believe that structured notes are a great asset class that provide investors the unique capability to customize their risk/return tradeoff, the tradeoff between a structured note and a more conventional investment sometimes comes out in favor of the conventional investment. In the product analyzed today, the odds of receiving a better payout as compared to the equivalent conventional product yield seems low and also seems hard to predict no matter how bullish one might be in regards the market – due to the effect of correlation. As I have mentioned in a recent blog, investors need to fully understand a structured note before investing in it and ensure it is the right solution vs. conventional, simpler products.