Diversification in numbers: two assets, one smoother ride

The claim

"Don't put all your eggs in one basket" is easy to say. Here is the arithmetic that stands behind it, with invented numbers so every step can be checked.

Imagine two assets, A and B. Over four years they return:

Both average (20 − 10 + 15 − 5) ÷ 4 = 5% a year, and so does B: (−5 + 15 − 10 + 20) ÷ 4 = 5%. On the surface they are identical. Each has two good years and two bad ones. These are not real funds; the figures are chosen only to show the effect.

Holding either one alone

Take ₹1,00,000 in Asset A:

• Year 1: ₹1,20,000
• Year 2: ₹1,08,000
• Year 3: ₹1,24,200
• Year 4: ₹1,17,990

Asset B ends at the same place: 0.95 × 1.15 × 0.90 × 1.20 = 1.1799, or ₹1,17,990. Both turn ₹1,00,000 into about ₹1,18,000, a compound rate near 4.2% a year, below the 5% simple average. That gap is volatility drag.

Holding half in each

Now put half the money in A and half in B, and rebalance to 50:50 at the end of each year. Each year's portfolio return is the average of the two:

Compound it: 1.075 × 1.025 × 1.025 × 1.075 = about 1.214. ₹1,00,000 becomes roughly ₹1,21,400, against ₹1,17,990 for either asset alone. That is about ₹3,400 more, with no extra risk taken.

The simple average is still 5%. Nothing about expected return changed. What changed is that the portfolio never had a losing year, and the compound rate rose to about 5.0% because there was almost no drag.

What made it work

The two assets moved in opposite directions. When A fell 10% in year two, B rose 15%. The blend absorbed the shock.

That is the whole mechanism, and it shows where diversification fails. If A and B had fallen in the same years, the blend would have fallen too, and the arithmetic would offer no help. Two funds holding the same stocks are a basket with the eggs still together; see mutual fund overlap.

What to take from it

• Look for different drivers, not more names. Holding five large-cap funds is not five baskets. Equity, debt and gold tend to respond to different things.
• Rebalancing is part of the effect. The example resets to 50:50 each year. Let one asset run and the blend drifts back towards that asset's risk. See rebalancing with new money.
• Real assets are noisier. Real correlations are rarely as neat as opposite years. Diversification narrows the swings; it does not remove them.
• The cost is a lower top. In this example the blend never made +20% in a year. Smoothness trades away the best years along with the worst.

You can try your own mix on the asset allocation calculator.

In short

Two assets with identical averages can combine into something better than either, but only when they do not fall together. The benefit is a smaller swing and a higher compounded return, not a higher expected return.

This post is educational, not financial advice. The returns above are invented for illustration and are not forecasts or the record of any asset.