Expected Portfolio Return
Also written Expected rate of return for a portfolio · Portfolio expected return · Ex-ante portfolio return · E(Rport)
The weighted average of the expected returns of the holdings in a portfolio, each weight being that asset's share of portfolio value — the return half of Modern Portfolio Theory.
In plain language
A portfolio return is much simpler than a portfolio risk, and it helps to see why.
Expected portfolio return is just a weighted average. Take each holding. Multiply its expected return by the share of the portfolio it occupies. Add the results up. That is the answer.
Nothing else enters. It does not matter whether the holdings move together or apart. Correlation has no effect at all on the return side.
That is the whole asymmetry at the heart of Modern Portfolio Theory. Return adds up in a straight line. Risk does not. Mix two assets that move apart and the portfolio risk falls below the weighted average of their risks. The portfolio return stays exactly on the weighted average.
So diversification is close to a free lunch. You keep the average return and you lose some of the average risk.
One caution on the word expected. This is a forecast built from probabilities, not a record of what happened. The workbook calls it an ex-ante return. Returns worked out from past data are ex-post.
How it works
The formula is section 4.6 of the workbook:
E(Rportfolio) = Σ Wi × E(Ri)
where Wi is the per cent of the portfolio held in asset i, and E(Ri) is the expected rate of return for that asset. The weights are determined by the proportion of value in the portfolio.
Where the asset-level input comes from. Section 4.4 builds it first: the expected rate of return of an individual investment is the sum of the expected returns multiplied by their corresponding probabilities. The workbook's own illustration forecasts Stock A at 15% in a boom (probability 0.3), 10% in a normal state (0.5) and 2% in a recession (0.2), giving 9.9%.
The workbook's portfolio table (Table 4.3), four assets:
| Weight | Expected return | Contribution |
|---|---|---|
| 0.2 | 9% | 0.018 |
| 0.1 | 12% | 0.012 |
| 0.3 | 15% | 0.045 |
| 0.4 | 18% | 0.072 |
| 1.0 | 0.147 = 14.7% |
The same formula with a risk-free asset. Chapter 5 reuses it to build the Capital Market Line: E(Rport) = WRF × RFR + (1 − WRF) × E(Ri). With a risk-free return of 5%, a risky return of 12% and 70% in the risk-free asset, the portfolio return is 7.10%. Borrow 50% of your wealth at the risk-free rate and put the lot into a market portfolio returning 20%, and the workbook computes (1.5 × 20%) − (0.5 × 5%) = 27.5%.
Where the number is used later. Chapter 9 feeds it straight into the risk-adjusted measures. In both the Sharpe ratio, (Rp − Rf) ÷ σp, and the Treynor ratio, (Rp − Rf) ÷ β, the Rp term is the expected portfolio return.
A worked example
Sahyadri Multi Asset Fund has a corpus of Rs 500 crore allocated as follows.
| Holding | Amount (Rs cr) | Weight | Expected return | Contribution |
|---|---|---|---|---|
| Unlisted growth equity | 200 | 0.40 | 22% | 8.80% |
| Listed large-cap equity | 150 | 0.30 | 14% | 4.20% |
| Private credit | 100 | 0.20 | 11% | 2.20% |
| Treasury bills | 50 | 0.10 | 6% | 0.60% |
| Total | 500 | 1.00 | 15.80% |
The expected portfolio return is 15.80%, or Rs 79 crore on Rs 500 crore.
Now shift the weights. The manager moves Rs 50 crore from treasury bills into unlisted growth equity. Weights become 0.50, 0.30, 0.20 and nil.
New return = (0.50 × 22%) + (0.30 × 14%) + (0.20 × 11%) = 17.40%.
The gain of 1.60 percentage points comes only from re-weighting. No holding changed its own expected return.
And the point of the exercise. The fund's standard deviation does not move in the same tidy way. Section 4.7 shows portfolio risk depends on the weights, the individual risks and the covariance of every pair. Selling the T-bills removed the one holding whose correlation with the rest was near zero, so the risk rose by much more than 1.60 points of return justifies. Return is a weighted average; risk is not.
Feed the result into the Sharpe ratio with a 364-day T-bill rate of 5.60% and a portfolio standard deviation of 9%: (15.80 − 5.60) ÷ 9 = 1.13.
Why NISM asks about it
Chapter 4 (Introduction to Modern Portfolio Theory), section 4.6, states the formula and works Table 4.3 to 14.7%. Chapter 5 reapplies it to the Capital Market Line with the risk-free asset, and Chapter 9 uses Rp as the numerator input to the Sharpe and Treynor ratios.
Expect a calculation question: you are given four or five weights and expected returns and asked for the portfolio return. It is a weighted average and nothing more, so the marks are lost only by mixing up weights with returns or by forgetting that the weights must sum to 1. The conceptual question that goes with it is the one worth learning — that correlation affects portfolio risk but never portfolio return.
Common exam traps
- Correlation does not enter the return formula at all. It enters only the risk formula in section 4.7. A question that gives you a correlation coefficient and asks for the portfolio return is testing whether you know to ignore it.
- Weights are shares of value, not equal shares. Four holdings do not mean weights of 0.25 each.
- Expected return is ex-ante; historical return is ex-post. The workbook names both. Do not compute one and label it the other.
- The individual asset input is itself probability-weighted. Section 4.4 sums return times probability. Skipping that step and averaging the scenario returns gives the wrong figure.
- With borrowing, one weight goes above 1 and another goes negative. The workbook's levered example is (1.5 × 20%) − (0.5 × 5%), not (1.5 × 20%) + (0.5 × 5%).
- Rp in the Sharpe and Treynor ratios is this number, not the realised return of the last twelve months.
Check yourself
1.A fund holds 15 per cent in a stock of beta 1.2 and 85 per cent in a stock of beta 1.5. With a risk-free rate of 6 per cent and a market risk premium of 10 per cent, the expected portfolio return is:
- a)20.55 per cent
- b)21 per cent
- c)18 per cent
- d)20 per cent
Show the answer
Answer: (a) 20.55 per cent
This is the workbook's own case study, whose explanation reads: Use Portfolio beta as a weighted average beta (0.151.2) + (0.851.5) = 1.455. Then using CAPM approach the expected return is 6% + (1.455 * 10%) = 20.55%. The step candidates miss is the first — portfolio beta is a simple weighted average of component betas. That works because beta captures only systematic risk, which cannot be diversified away, so unlike portfolio standard deviation there is no covariance term to add.
Where this is taught
Free preparation for NISM Series XIX-CRelated terms
- CAPMA model that prices the return an investor should demand from a share: the risk-free rate plus beta times the market risk premium.
- Standard deviationA measure of how far returns typically stray from their own average — the standard statistic for total risk, counting company-specific and market-wide causes alike.
- Portfolio betaThe weighted average of the betas of the holdings in a portfolio — the measure of its systematic, non-diversifiable risk used in CAPM, the Treynor ratio and market-neutral strategies.
- CorrelationA measure of the strength and direction of the relationship between two variables, running from -1 to +1, and the single factor that determines how much risk diversification actually removes.
- CovarianceA measure of the degree to which the returns of two assets move together relative to their own averages — the building block of portfolio risk, standardised into the correlation coefficient.
- Expected utilityThe satisfaction score an investor is assumed to assign to each possible outcome of an investment, weighted by the probability of that outcome — the quantity Modern Portfolio Theory assumes investors actually maximise.
- Variance-covariance matrixThe grid of every asset's variance and every pair's covariance that is needed to compute the risk of a portfolio holding more than two securities.
- Risk Aversion IndexThe 'A' in the Markowitz utility formula U = E(r) − 0.5 × A × σ² — a number capturing how heavily an individual investor's utility is penalised for taking on variance.
- Variance of a SecurityThe probability-weighted average of the squared gaps between a security's possible returns and its expected return — the forward-looking measure of a single asset's risk in Modern Portfolio Theory.