Private Wealth Management puzzles, solved step by step
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055Rs 50 lakh sits in the regular plan of a mutual fund, which charges 0.8% a year more than the direct plan of the same fund. If the direct plan compounds at 11% a year after its own costs, what is the gap in ending wealth after 20 years?Mutual fund distributionIndian wealth management
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Roughly how large is the gap after 20 years?
Show the worked solution
About Rs 54 lakh. At 11% the direct plan grows Rs 50 lakh to about Rs 403.1 lakh in 20 years. At 10.2% the regular plan reaches about Rs 348.8 lakh. The gap is Rs 54.3 lakh, 13.5% of the direct plan's ending value, from a cost difference that sounds like less than one per cent.
Why is the gap so much larger than 0.8% sounds?
A slow leak in a water tank loses a little each hour, but it keeps leaking from a tank that is also being filled, and every litre lost is a litre that never reaches the tap. An annual fee is charged on the whole growing balance every year, and each rupee taken stops compounding for the rest of the period. Charged only on the starting Rs 50 lakh, 0.8% for 20 years would be Rs 8 lakh. Charged on a balance that grows several times over, it is Rs 54 lakh.
Rs 50 lakh in the direct plan at 11% and the regular plan at 10.2% ends Rs 3.0 lakh apart after 5 years, Rs 9.9 lakh after 10 and Rs 54.3 lakh after 20, because the fee gap compounds along with the money. How do you estimate it without a calculator?
Use the ratio of the two growth factors. Each year the regular plan keeps 1.102 / 1.11 of what the direct plan keeps, about 0.9928, so it loses roughly 0.72% of the direct plan's value a year. Over 20 years that compounds to about 1 minus 0.9928 to the 20th, roughly 13.5% of the ending value. The direct plan ends near Rs 400 lakh, so the gap is a little over Rs 50 lakh. Two lines of arithmetic, and the answer is within a lakh or two.
The relationship50 the investment, Rs lakh 1.11 one year of growth in the direct plan 1.102 one year of growth in the regular plan, 0.8% lower What it says in wordsThe gap is the same money compounded at two rates for 20 years, subtracted.Be fair to the regular plan when you say this to a client. The extra cost pays the distributor, and some investors value the advice and service they get for it. The numeracy point is only that the price of that service, over 20 years, is measured in tens of lakhs, and the client should see it in rupees before deciding.
Where candidates lose it
The fast wrong answer is 0.8% x Rs 50 lakh x 20 years, Rs 8 lakh. It charges the fee only on the starting amount and ignores that each rupee of fee also loses its future growth.
The second miss is presenting the gap as proof that one plan is bad. The interviewer wants the number and a fair sentence on what the extra cost buys.
What the interviewer asks next
- What share of the ending value is lost if the gap is 1.5% a year instead of 0.8%?
- How does the answer change for a monthly SIP of Rs 50,000 instead of a lump sum?
- What would a client get for the extra cost in a regular plan, and how would you judge whether it is worth it?
079An equity fund keeps 10% of its money in cash, earning 6%, while the stocks it holds return 14%. How much does the cash cost the fund's return each year?Mutual fund distributionIndian wealth management
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How much return does the cash cost?
Show the worked solution
About 0.8 of a point a year. The fund earns 90% x 14% plus 10% x 6%, which is 12.6 plus 0.6, or 13.2%. Fully invested it would earn 14%. The drag is the cash weight times the gap in returns: 10% x (14 - 6) = 0.8 of a point, in a year when stocks beat cash.
Where does the 0.8 of a point come from?
Picture a shop with ten shelves, nine stocked with goods that earn a good margin and one kept empty as a buffer for a delivery that may come. The empty shelf is not free: it costs the margin it would have earned. Cash drag is the cash weight times the gap between what cash earns and what the invested money earns. Here that is 10% times 8 points, or 0.8 of a point.
Stocks at 90% of the fund earning 14% contribute 12.6 points and cash at 10% earning 6% contributes 0.6, a blended 13.2% that is 0.8 of a point below the 14% a fully invested fund would earn. The relationshipw_cash the share of the fund held in cash, 10% r_stocks the return on the invested stocks, 14% r_cash the return on cash, 6% What it says in wordsThe cost of idle cash is its weight times the return it gives up.Is the cash ever worth it?
Yes, and say so. In a year when stocks fall 10%, the same fund loses 8.4% rather than 10%, so the cash cushions. It also pays redemptions without forcing the manager to sell into a falling market. Cash drag is a cost in rising markets and a cushion in falling ones, so the question for a client is whether the manager holds cash on purpose or by accident. A fund that is always 10% in cash is charging an equity fee on money sitting in a deposit.
Scale it up to show the stakes: 0.8 of a point a year compounds. Rs 1 crore at 14% for ten years grows to about Rs 3.71 crore; at 13.2% it grows to about Rs 3.45 crore.
Where candidates lose it
Candidates often answer 0.6 of a point, confusing what the cash earns with what it costs, or 1.4 points, a tenth of the stock return, forgetting the cash still earns something.
The other loss is calling cash pure waste. Say the drag, then say the cushion in a falling year: the interviewer wants to hear that you see both sides of the same holding.
What the interviewer asks next
- Stocks return minus 10% this year. What does the fund return?
- At what stock return does the cash stop being a drag?
- How would you check whether a fund's cash level is deliberate?