A fund house wants a fund of funds across Indian equity, international equity, short-term debt, gold and a listed REIT, with no sleeve above 40%, for a moderate-risk investor. Propose weights, then assess an underlying equity fund that returned 13.1% against a 12.4% benchmark with a beta of 1.25 while cash paid 6.5%.

Propose 35% Indian equity, 15% international equity, 30% short-term debt, 10% gold and 10% REIT, and do not accept the equity fund on its headline record. The mix targets about 9.3% at 8.7% volatility, against 10.0% at 10.8% for a plain 60/40. The equity fund beat its benchmark by 0.7 points, but with a beta of 1.25 it should have earned 13.87%, so its Jensen's alpha is about -0.8%: it was paid for leverage to the market, not for skill.

Give each one a job before giving it a weight. A kitchen with five burners is not improved by putting every pot on the hottest one. Indian equity is the main growth engine, international equity adds growth from economies and currencies that do not move with India, short-term debt carries the portfolio through falls and funds redemptions, gold tends to hold up when equities and the rupee fall, and the REIT adds rental income tied to a different cycle. A moderate investor needs enough equity to beat inflation over five years and enough stability to stay invested through a 30% fall, which points to about half the money in equity.

35% Indian equity, 15% international equity, 30% short-term debt, 10% gold and 10% REIT. Equity totals 50%, below the 40% cap in any one sleeve, and international equity at 15% is meaningful without letting currency drive the result. On the stated assumptions the mix has an expected return of about 9.35% and volatility of about 8.7%, against 10.0% and 10.8% for a plain 60/40 Indian equity and debt fund. It gives up 0.65 points of expected return for about 2.1 points less volatility, the trade a moderate investor is buying. Gold and the REIT are capped at 10% each because their long-run returns are lower and the REIT market is small and concentrated.

Strip out the risk it took. A beta of 1.25 means the fund moved 1.25 times as much as its benchmark, so in a rising market it should beat the benchmark without any skill at all. Jensen's alphaThe return a fund earned above what its beta would predict: fund return minus the risk-free rate minus beta times the market's return over the risk-free rate. measures what is left. Expected return for that beta is 6.5% + 1.25 x (12.4% - 6.5%) = 13.875%; the fund made 13.1%, an alpha of about -0.77%. It beat the benchmark because the market rose and it carried more of the market, and it was paid less than that extra risk would have earned.

Close with the decision and its limits. Do not put this fund in the Indian equity sleeve on its record; a high-beta fund in a rising five-year period will almost always look good against its benchmark and will fall harder when the market turns, which is the opposite of what a moderate-risk fund of funds wants. Look for a fund with positive alpha and beta near 1, or use a low-cost index fund for the sleeve. The limits: five years is a short window for alpha, beta itself moves over time, and the asset-class assumptions are judgement, so the weights should be tested against a range of return and correlation assumptions, and the extra layer of fees in a fund of funds counted before launch.