1. What you will learn
By the end of this lesson you will be able to compute a portfolio's return from weights rather than by averaging, explain why correlation and not merely the number of holdings determines diversification, calculate a two-asset portfolio's variability at different correlations, and measure true exposure by looking through funds to what they actually hold. This is education about portfolio arithmetic and is not advice about any allocation, fund or security.
2. The idea explained
A portfolio's return is a weighted average, not a simple one. Each holding contributes its own result multiplied by the share of capital it represents, and those contributions are added. Averaging the results of the holdings without regard to size is wrong whenever the weights differ, which is almost always.
Diversification is the second idea and it is widely misunderstood. Holding more names reduces the damage any single one can do, but it does nothing about the risk that all of them share. Two holdings that move almost identically provide almost no diversification however different their names, while two that move differently provide a great deal. The quantity that captures this is correlation, and it enters the arithmetic of portfolio variability directly.
For two assets, the portfolio's variance is the first weight squared times the first variance, plus the second weight squared times the second variance, plus twice the product of the two weights, the correlation and the two standard deviations. The third term is where diversification lives. When correlation is one, the expression collapses and the portfolio's variability is exactly the weighted average of the two, so nothing has been gained. As correlation falls, that third term shrinks, and the portfolio becomes less variable than its parts.
Three distinctions keep the subject honest. Asset allocation is the decision about how much sits in each broad class. Security selection is the decision about which holdings within a class. Market timing is the decision about when to hold them at all.
Finally, measure what you actually own. A portfolio holding several funds may own the same underlying companies many times over, and a portfolio of many names drawn from one sector remains a concentrated bet on that sector. Look through every fund to its holdings and add up the real exposure by sector, by size and by geography, because the number of line items on a statement says nothing about concentration.
3. The market, the regulator and the rulebook
Mutual funds and exchange-traded funds in India are regulated by the Securities and Exchange Board of India, the statutory securities regulator constituted by an Act of Parliament, under its regulations governing mutual funds. Those regulations set out how schemes are categorised, what they may hold, how net asset value is computed and what must be disclosed.
Every scheme publishes a scheme information document and a key information memorandum setting out its objective, its permitted universe and its risk factors, and publishes its portfolio holdings periodically.
The industry body for asset managers publishes aggregated data, and the exchanges publish index methodologies against which schemes are measured. Never state an expense ratio, a category limit, a tax rate or an exit load as a fixed fact; describe how each works and name the document publishing the current figure, with the date you read it.
Worked example
4. Worked example
All figures are invented. A portfolio holds sixty per cent in a hypothetical asset A and forty per cent in a hypothetical asset B. Over one period A returns ten per cent and B returns minus five per cent.
The portfolio return is zero point six multiplied by ten, which is six, plus zero point four multiplied by minus five, which is minus two, giving four per cent before costs.
Now test the wrong method. Averaging ten and minus five gives two and a half per cent, which is not the answer, because it treats a sixty-rupee holding and a forty-rupee holding as though they were equal.
Now variability. Suppose A has a standard deviation of twenty per cent and B of twelve per cent. The weighted average of those is zero point six times twenty plus zero point four times twelve, which is sixteen point eight per cent, and that is what the portfolio's variability would be if the two moved identically.
Take a correlation of zero point three. The variance is zero point three six multiplied by zero point zero four, which is zero point zero one four four, plus zero point one six multiplied by zero point zero one four four, which is about zero point zero zero two three, plus twice zero point six times zero point four times zero point three times zero point two zero times zero point one two, which is about zero point zero zero three five. The total is about zero point zero two zero two, and its square root is about fourteen point two per cent.
Now set the correlation to zero. The third term vanishes and the variance becomes about zero point zero one six seven, whose square root is about twelve point nine per cent. The same two holdings in the same proportions produce sixteen point eight, fourteen point two or twelve point nine per cent of variability depending only on how they move together.
Finally, look-through. Suppose half the portfolio sits in a fund that holds thirty per cent in one sector, three-tenths in a fund that holds sixty per cent in the same sector, and the remaining fifth directly in that sector. The true exposure is zero point five times zero point three, plus zero point three times zero point six, plus zero point two times one, which is fifteen plus eighteen plus twenty, or fifty-three per cent in a single sector.
5. Common mistakes and how to fix them
The first mistake is averaging returns instead of weighting them. Multiply each result by its share of capital and add.
The second is counting holdings as a measure of diversification. Compute or estimate correlations, and note that a low number of holdings with low correlation can be better diversified than a long list with high correlation.
The third is ignoring fund overlap. Look through to holdings and aggregate exposure by sector, size and geography.
The fourth is mixing allocation, selection and timing. Keep the three decisions and their evidence separate.
The fifth is treating diversification as protection against loss. It reduces concentration, not the risk that a whole market falls. Past performance does not indicate future results, no allocation is safe or guaranteed, and a SEBI-registered investment adviser is the person to consult about an individual's own money.
Key takeaways
6. Board summary
Portfolio return is the sum of each holding's result multiplied by its share of capital, never a simple average. Two-asset variance is the sum of the squared weight and variance terms plus twice the weights, correlation and standard deviations. When correlation is one the portfolio is exactly as variable as the weighted average of its parts; diversification appears only as correlation falls. Allocation, selection and timing are three separate decisions requiring separate evidence. Look through every fund to its holdings, because the number of line items says nothing about concentration.
Check your understanding
7. Practice and self-check
One. Seventy per cent in an asset returning eight per cent and thirty per cent in one returning minus four per cent. Portfolio return? Five point six less one point two, which is four point four per cent.
Two. What would a simple average have given? Two per cent.
Three. Why is that wrong? Because it ignores the unequal capital weights.
Four. Standard deviations are eighteen and ten per cent. What is the weighted average? Fifteen point six per cent.
Five. If the correlation were one, what would the portfolio's variability be? The same fifteen point six per cent.
Six. Does a portfolio of forty holdings from one sector have low concentration? No; the count is irrelevant if they move together.
Seven. A portfolio has forty per cent in a fund holding a quarter in one sector, forty per cent in a fund holding half in that sector, and twenty per cent directly in it. True exposure? Ten plus twenty plus twenty, which is fifty per cent.
Eight. Which decision is being made when you choose how much sits in equities overall? Asset allocation.
Nine. Where do you find a fund's actual holdings? Its periodic portfolio disclosure, cited with the date read.