Portfolio Size Matters

3/17/2014


Newsletters like the Forecasts devote most of their space toward presenting stocks ripe for purchase. Such a focus makes sense because you, the reader, wouldn't subscribe unless you shared our interest in stock selection.

But finding good stocks isn't the only step on the journey. To craft a winning portfolio, you must also consider ways to limit risk.

Limiting risk with stock count

In our study, the 60,000 one-stock portfolios (1,000 portfolios in each of 60 quarters) of high Overall scorers within the S&P 500 delivered a quarterly standard deviation of 16.2%, meaning that about two-thirds of returns were between 16.2% above the average and 16.2% below the average. In other words, we can say that the returns fell within a 32% range two-thirds of the time, which is almost useless as an investment tool.

However, bump the portfolio size up to 10 stocks, and the standard deviation shrinks to 4.9%, less than one-third of the one-stock portfolios' volatility. Add another 10 stocks, and the standard deviation falls to 3.3%, about one-fifth that of the one-stock portfolios.

Adding another 20 stocks, for a total of 40 stocks, reduced standard deviation to 2.0%, or 12% of the one-stock portfolios. By this point, adding stocks only lowers risk slightly. An 80-stock portfolio had a standard deviation of 0.8%, or 5% of the one-stock portfolio.

Based on our likelihood-of-loss data, the benefits of adding stocks are largely exhausted after about 20 stocks. In our back-test of top Overall scorers in the S&P 500, 41% of the one-stock portfolios posted a quarterly loss, versus 31% of 10-stock portfolios and less than 30% of 20-stock portfolios. The likelihood of loss declines only slightly after 20 stocks.

For top scorers among smaller stocks in the S&P 600 Index, likelihood of loss doesn't decline at all after 40 stocks, and a 20-stock portfolio is only slightly worse at avoiding losses.

Our Upside newsletter, which focuses on small-cap stocks, targets 35 to 40 stocks for its Buy List, with about half on the more focused Best Buy List. The Forecasts Buy List targets 25 to 30 stocks, of which about half are on the Focus List.

Of course, if you purchased stocks without taking Quadrix scores into account, you'd need larger portfolios to diversify.  

MORE STOCKS, LESS RISK
Adding stocks to a portfolio reduces volatility, as measured by standard deviation. While the small-cap stocks in the S&P 600 Index tend to be riskier than the large-caps in the S&P 500, increasing the number of stocks diversifies both types of stocks in the same way. You reap the biggest diversification benefit jumping to a 10-stock portfolio from a one-stock portfolio. All of the data below stem from a back-test of 1,000 randomly generated portfolios for each of the 60 quarterly periods from January 1999 to December 2013.
------------ S&P 500 Index ------------
------ S&P SmallCap 600 Index ------
------ Quadrix Overall Quintile ------
-------Quadrix Overall Quintile -------
Stocks In
Portfolio
Top
(%)
Middle
(%)
Bottom
(%)
Top
(%)
Middle
(%)
Bottom
(%)
Standard deviation
1
16.2
13.6
21.6
20.4
19.8
30.4
10
4.9
4.1
6.5
6.2
6.0
9.3
20
3.3
2.8
4.4
4.2
4.1
6.2
40
2.0
1.7
2.6
2.6
2.6
3.9
60
1.3
1.1
1.8
1.9
1.8
2.8
80
0.8
0.7
1.1
1.3
1.3
1.9
 
You can also measure volatility by the likelihood of loss, in this case the percentage of portfolios which posted quarterly declines during our 15-year study. Based on both standard deviation and likelihood of loss, we conclude that investors in large-cap stocks have captured most of the available diversification benefit by the time they've acquired 20 stocks. A little more diversification is necessary for the optimal small-cap portfolio.
Likelihood of loss
1
40.7
42.2
43.3
42.5
43.5
46.5
10
31.1
36.8
38.7
33.9
37.6
40.8
20
29.5
35.8
37.5
32.4
36.4
39.5
40
28.5
35.3
37.0
31.6
35.3
38.3
60
27.8
35.6
36.7
31.7
35.0
37.7
80
26.7
35.8
36.8
31.8
34.6
36.9
 
Tracking error measures risk in another way, the average absolute difference between the returns of individual portfolios and the average return for all of the portfolios. For example, suppose the random portfolios of high-scoring S&P 500 stocks matched the average 3.3% return of the top quintile. The one-stock portfolios' tracking error suggests the average portfolio delivered a return 11.3 percentage points away from the average. However, tracking error falls to a manageable 2.4% by the time you reach 20-stock portfolios.
Tracking error
1
11.3
9.8
14.6
15.0
13.9
20.2
10
3.6
3.1
4.8
4.8
4.6
6.8
20
2.4
2.1
3.3
3.2
3.1
4.6
40
1.5
1.3
2.0
2.0
2.0
2.9
60
1.0
0.9
1.3
1.4
1.4
2.0
80
0.6
0.5
0.8
1.0
1.0
1.4


What this means for you

The appropriate level of risk varies based on the goals, preferences, and time horizon of each investor. Some investment methods lend themselves to a broad portfolio, while others work better with a more focused approach. As such, there is no perfect number of stocks that works for everyone.

Only you can determine whether your portfolio is properly diversified. To do that, ask yourself the following questions:

How much risk can I tolerate? Our 15-year study of quarterly returns can provide some perspective. Two-thirds of the 10-stock portfolios of top Quadrix scorers from the S&P 500 managed quarterly returns within a 9.8% range. If those portfolios matched the average quarterly return of 3.3% for such high-scoring stocks, we would be looking at total returns ranging from -1.6% to 8.2% in two-thirds of the quarters. Using the same assumptions, a 40-stock portfolio (standard deviation of 2.0%) would have delivered quarterly returns of 1.3% to 5.3% two-thirds of the time.

Do I have enough stocks? Compare your current portfolio to your risk tolerance. If you own too many stocks, consider selling some of the weaker names. If you don't own enough, peruse our recommended lists for ideas. Remember, diversification is the one free lunch available on Wall Street. Up to a point, you can lower risk without lowering expected return by adding stocks. At some point, adding more stocks won't lower risk much — and may require that you settle for second-tier opportunities. Still, you are likely to do better focusing on finding 25 to 35 stocks you truly love rather than searching for one stock on which to bet your entire portfolio.

Do my stocks score well in Quadrix? Quadrix rewards stocks with broad-based fundamental strength (read: high-quality stocks with attractive valuations). High scorers are less risky than the average stock. If you follow our recommended lists, or even if you don't track our lists but do use Quadrix to select your own stocks, you should not need more stocks than the number we recommend (25 to 30 large-caps and midcaps, 35 to 40 small-caps) to diversify.

Is my portfolio diverse enough? While this story focuses on portfolio size, no discussion of diversification is complete without addressing sector weightings. By spreading your stocks among different sectors and industry groups, you can reduce your risk.

If you are worried about benchmark risk (the risk of deviating from an index), it makes sense to tie diversification to an index. But if you are worried about the actual risk of your portfolio (either volatility or risk of loss), it does not really matter whether the utility sector is 3% or 30% of the index. What matters is how much of your portfolio is tied to the utility sector, and whether you could lower your portfolio's overall risk by adding or dropping a utility stock.

Looking for sector-diversification ideas? Here is a top selection from each of the 10 sectors. All but the telecom name are pulled from our buy lists. We don't currently recommend any telecoms for purchase, but we rate Verizon Communications ($47; VZ) as an A (above average) on our Monitored List.

• Consumer discretionary: Magna International ($97; MGA).
• Consumer staples: Kroger ($43; KR).
• Energy: Helmerich & Payne ($98; HP).
• Financials: Wells Fargo ($48; WFC).
• Health care: Express Scripts ($79; ESRX).
• Industrials: United Rentals ($90; URI).
• Materials: Dow Chemical ($49; DOW).
• Technology: Skyworks Solutions ($36; SWKS).
• Telecom services: Verizon Communications ($47; VZ).
• Utilities: UGI ($44; UGI).


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