Your Portfolio Has 20 Holdings. It May Behave Like Only 3. How to Count Your Real Number of Bets
5 min read
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5 min read
You own 20 stocks. Rp 5,000,000 in each, Rp 100,000,000 in total. That feels safe.
Then the market drops and all 20 fall together. Your "20 different bets" turned out to be one big bet wearing 20 name tags.
This post shows how to count your effective number of bets: how many truly independent risks your portfolio really holds. With one simple formula, you will see why 20 holdings can behave like only 3.
A bet is one independent source of risk. Two stocks that always move together are one bet, not two.
The effective number of bets is the count of equal, independent bets that would give you the same level of risk as your actual portfolio. The idea comes from Attilio Meucci's 2009 paper "Managing Diversification". His version uses entropy and principal components, which is heavy maths.
You do not need that to get the main lesson. Below is a simplified version that uses one input: correlation.
Correlation is a number from -1 to +1 that says how much two prices move together. At +1 they move in lockstep. At 0 they ignore each other. Below 0 they tend to move in opposite directions.
Take a simple case. You hold N assets, all the same size. Each one is equally bouncy (same volatility, meaning how far its price swings). Every pair has the same correlation, called ρ.
This is NetWort's own simplification of the idea, not Meucci's formula. It comes straight from the standard variance of an equal-weight portfolio. Real portfolios have unequal weights and unequal correlations, so treat the result as a guide, not a measurement.
Here is the formula applied to your 20 stocks. The last column shows how bumpy the whole portfolio is compared with a single holding.
| Average correlation (ρ) | Effective bets | Portfolio swings, as % of one stock's swings |
|---|---|---|
| 0.0 | 20.0 | 22% |
| 0.1 | 6.9 | 38% |
| 0.3 | 3.0 | 58% |
| 0.5 | 1.9 | 73% |
| 0.8 | 1.2 | 90% |
These correlations are illustrative. They are not measured from real stocks.
Read the row for 0.3. Twenty holdings act like 3 bets. Your portfolio still swings at 58% of one stock's level, so most of the risk never went away.
At 0.8, owning 20 stocks cuts your swings by only 10%. You paid the effort of 20 positions for almost no benefit.
Look at what happens when N gets very large. The formula gives a limit of 1 ÷ ρ.
At an average correlation of 0.3, the most you can ever reach is about 3.3 effective bets. That holds whether you own 20 stocks or 2,000.
So adding the 21st stock to a basket of similar stocks barely helps. Adding something that moves differently does far more. Our guide on how many stocks you need for diversification covers the count side, and stock correlation and diversification goes deeper on the correlation side.
Another way to measure the same thing is the diversification ratio. Yves Choueifaty and Yves Coignard introduced it in their 2008 paper "Toward Maximum Diversification".
It divides the average volatility of your holdings by the volatility of the whole portfolio. A ratio of 1 means no diversification benefit at all. A higher number means more.
In our equal-weight case, the diversification ratio equals the square root of the effective number of bets. At ρ = 0.3 that is about 1.7. In plain words, your portfolio is roughly 1.7 times calmer than its average holding.
One warning. Correlation changes. It often rises when markets fall, which is the exact moment you wanted diversification to work.
So a portfolio that looks like 6 bets in a calm month may behave like 2 in a crash. Our post on correlation breakdown in a market crash shows how this plays out.
Also, the formula says nothing about size. Rp 80,000,000 in one sector and Rp 20,000,000 across everything else is concentrated, whatever the count says. See portfolio concentration risk.
You can run the same check in three steps.
NetWort does not draw a pairwise correlation table yet, so this step is a judgement call. But it gives you two numbers that help. Open the Portfolio Health section of your dashboard and look at your portfolio's volatility and beta together. Then open an asset page, for example BBCA, Bank Central Asia, to see how that holding's S&P 500 correlation reads.
If your volatility is close to that of your single biggest holding, you may have fewer bets than you think. For a view of how the wider market is moving today, the Market page is a good next stop.