Analyst Spotlight Archive

Analyst Spotlight: Benjamin King

Holdings-based analysis is fairly straightforward; as its name suggests, it involves analyzing the actual underlying holdings of a fund. Its main advantage is that it is accurate in determining a fund’s attributes. However, it has a couple notable disadvantages.

First is a lack of timeliness. Most commonly, we only receive new holdings data on funds on a monthly or even a quarterly basis. In today’s volatile markets, a lot can change for a fund in just a few months. This can be particularly important, for instance, when there is a change in a fund’s manager or investment process.

Another disadvantage to holdings-based analysis is a lack of standardization in how firms report their funds’ exposures. For example, one firm’s definition of technology stocks may be different than another’s. This can make analysis difficult and inefficient.

That is where returns-based analysis becomes valuable, because its major advantages are timeliness and standardization. By analyzing the returns of a fund (along with various indexes) we can gather some of the same information as in holdings-based analysis, but on a daily, weekly and monthly basis in standardized formats. The main disadvantage of this approach is that the information gleaned from examining returns may be less accurate. We are trying to infer fund attributes by looking at how the fund behaves, rather than determining its attributes from what it actually owns.

A Simple Concept
In concept returns-based analysis is really pretty simple. For example, imagine you are looking at two funds, one is a bond fund and one is a stock fund, but you don’t know which is which. You probably would not have to watch their daily returns for very long, against the backdrop of the performance of the overall stock and bond markets, to make a very accurate guess as to their true identities.

“Okay, I can see that,” you might say, but “what kind of information can you actually draw from returns?”

There is actually a tremendous amount of information that can be drawn from analyzing return streams. On the simplest level, we can get such basic information as how it is performing versus its peers. And by using some simple calculations, such as correlation and standard deviation, we can assess a fund’s volatility and how it it’s likely to move in relation to various indexes and other funds.

But, by employing some more sophisticated analysis, we may find insight into such things as: what areas of the market a fund is favoring; changes in fund strategy and asset allocation; as well as how well the manager is picking stocks within their particular investment universe.

Example: Estimating a Fund’s Asset Allocation
While the actual mathematics behind this, called regression analysis, can be very intricate, the basic ideas are fairly accessible. Regression is simply a statistical method of finding an equation that best describes the relationship between a number of variables.

As an example let’s look at estimating a fund’s allocation among stocks, bonds and cash. As shown in the table below, the variables we consider here are the daily returns of the fund, the S&P 500 (proxy for stocks), the Lehman Aggregate Bond Index (proxy for bonds) and 3-Month T-Bills (proxy for cash).

	Daily Return %
			Lehman	3-Month
	Fund	S&P 500	Aggregate	T-Bill
11/2/2007	0.13	0.08	0.24	0.08
11/1/2007	-1.44	-2.62	0.44	0.04
10/31/2007	0.61	1.21	-0.39	0.01
10/30/2007	-0.39	-0.64	-0.03	0.02
10/29/2007	0.26	0.39	0.09	0.00
10/26/2007	0.78	1.38	-0.17	0.02
10/25/2007	-0.09	-0.10	-0.08	-0.01
10/24/2007	-0.04	-0.24	0.34	0.04
10/23/2007	0.55	0.88	0.05	0.03
10/22/2007	0.22	0.38	-0.01	-0.02
10/19/2007	-1.42	-2.56	0.39	0.01
10/18/2007	0.03	-0.07	0.20	0.07
10/17/2007	0.26	0.19	0.46	0.07
10/16/2007	-0.37	-0.66	0.08	0.02
10/15/2007	-0.48	-0.84	0.10	-0.01
10/12/2007	0.25	0.48	-0.12	0.01
10/11/2007	-0.30	-0.51	0.03	-0.01
10/10/2007	-0.09	-0.16	0.02	0.01
10/9/2007	0.50	0.81	0.04	0.00
10/8/2007	-0.19	-0.32	0.00	0.00
10/5/2007	0.44	0.98	-0.50	0.03
10/4/2007	0.17	0.21	0.13	0.01
10/3/2007	-0.26	-0.44	0.00	0.02
10/2/2007	0.03	-0.03	0.15	0.00
10/1/2007	0.83	1.33	0.10	-0.01
9/28/2007	-0.19	-0.30	-0.04	-0.01
9/27/2007	0.32	0.39	0.27	0.02
9/26/2007	0.34	0.56	0.02	0.02
9/25/2007	0.00	-0.03	0.04	0.02
9/24/2007	-0.30	-0.53	0.05	0.00

In a hypothetical world, where a fund could only invest in these three indexes and didn’t change its allocation in the time period in question, then it would be simple algebra to determine its weight in stocks (b1), bonds (b2) and cash (b3) using the formula:

where y represents the daily returns of the fund; x1 the daily returns of the S&P 500; x2 the daily returns of the Lehman Aggregate Bond Index; and x3 the daily returns of 3-Month T-Bills.

Of course, in the real world, things are not quite that simple; most obviously we know that a fund doesn’t really invest in those indexes, they are only proxies for the fund’s actual investments in individual stocks, bonds and cash. As a result, our formula won’t likely be able to find one asset mix that will actually yield the fund’s actual return each day. The way to work around this problem is to add an error factor (e), so the equation becomes:

What our returns-based analysis program does is to determine which set of values for the percentages in stocks, bond and cash (using the proxies), that yields the smallest average error term. For instance, using the sample daily return streams in the table, if we assume the fund had 30% in stocks, 70% in bonds and 0% in cash, then the average error term comes out to about 0.23 per day. But if we use 50% in stocks, 40% in bonds and 10% in cash, the average error term drops down to about 0.07. Our program will continue to tryout various combinations of allocations until it finds the one with the smallest average error term.

Since the error term represents the amount of the fund’s performance (return) that is not explained by an allocation to the three underlying asset classes, a very small average error term implies that a large proportion of the fund’s returns can be explained by the proposed asset allocation and thus it is more likely that it is close to the fund’s actual allocation.

The Next Step: Determining a Fund Manager’s “Selection” Return
Our in-house studies have found that a fund manager’s skill in selecting individual securities tends to persist over time more than other measures of manager skill. In other words, a manager who is good at picking stocks this year, will likely be good at picking them next year, and the year after that, as well. We can use returns-based analysis as one tool for evaluating the ability of managers to add value through stock selection.

In a similar manner to the way we determined a fund’s allocation to stocks, bonds and cash, we can determine within stocks, how much is allocated to large cap growth, or small cap value, etc. Knowing these underlying allocations, we can then determine a manager’s expected return for a given time period which represents a sort of custom index for the fund.

Again using a simple example, if a fund had 50% of its assets in large cap growth stocks and 50% in large cap value stocks, and over a given period, the average large cap growth stock returned 10.5%, while the average large cap value stock returned 5.2%, then the fund’s expected return would be (50% x 10.5%) + (50% x 5.2%), or 7.85%.

This prediction is known as the fund’s “Style Return.” If we subtract a manager’s Style Return from their total return, the difference is what the manager’s security selection is adding or subtracting from the fund’s performance. This is called the fund’s “Selection Return.” As shown in the example below, over roughly the 12 months ending last November, Fidelity Growth Discovery’s Selection Return (red line) has moved from near the bottom of its peer group (75th to 95th percentile) to the highest (5th to 25th percentile). We believe this was the result of a new manager, Jason Weiner, taking over, and it was one of the supporting factors in our decision to add Growth Discovery to our growth-oriented client portfolios in 2007.

In summary, while holdings based analysis is a standard and useful approach to evaluating funds, we believe complimenting that with less traditional, returns-based analysis can improve the timeliness of detecting important changes in the funds we consider for your portfolios.  

-- Benjamin King