Case 012Macro and multi-asset scenariosCore

The central bank cuts rates by 50 basis points. A fund holds Rs 300 crore of bonds at duration 5, where yields fall 40 basis points, and Rs 500 crore of equities at 20 times earnings with 6% growth, where the cost of equity falls 25 basis points. Estimate the gain on each.

PIMCOLos Angeles · 2024

The situation

The Reserve Bank cuts its policy rate by 50 basis points. Kaushiki Asset Allocation Fund holds Rs 300 crore of bonds with a modified duration of 5; the yields on those bonds fall 40 basis points. It also holds Rs 500 crore of Indian equities, priced at 20 times next year's earnings, with long-run earnings growth of 6% and a cost of equity of 11%.

The strategist estimates the cut lowers the cost of equity by 25 basis points, to 10.75%. Treat the equity market as a growing stream of payouts to shareholders.

Your task

Estimate the gain on the bond sleeve and on the equity sleeve, explain why one gains more, and say what could make the equity estimate wrong.

Quick check

Which sleeve gains more in rupees from the cut?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

About Rs 6 crore on the bonds and Rs 26 crore on the equities, if growth holds. Bonds gain duration times the yield fall: 5 times 0.40% on Rs 300 crore. Equities at 20 times earnings with 6% growth behave like an asset with a duration of about 20, so a 25 basis point fall in the cost of equity lifts the multiple to 21.05. The equity gain vanishes if the cut signals growth slowing by a quarter point.

Step 1How much do the bonds gain?

Use duration: a bond's price moves by about its duration times the change in yield. Rs 300 crore times 5 times 0.40% is Rs 6.0 crore. Note the yields fell 40 basis points, not 50: markets price cuts in advance and the longer end of the curve moves less than the policy rate, so always ask which yield actually moved.

Step 2Why do equities behave like a long bond?

Because an equity's value is a stream of payouts stretching decades ahead, and the further away a payment is, the more a change in the discount rate moves its present value. A house bought for its rent works the same way: when loan rates fall, buyers pay more for the same rent. With the market at 20 times earnings, the gap between the cost of equity and growth is 1 over 20, 5%, and the equity's durationThe percentage change in value for a one percentage point change in the discount rate. For a growing perpetuity it is 1 / (r - g). is about 1 over 5%, 20 years. A bond fund manager would call that very long.

The relationship
PE=1r−g:10.11−0.06=20  →  10.1075−0.06=21.05\frac{P}{E} = \frac{1}{r - g}: \quad \frac{1}{0.11 - 0.06} = 20 \;\to\; \frac{1}{0.1075 - 0.06} = 21.05
rcost of equity, 11% falling to 10.75%
glong-run growth of payouts, 6%
P/Eprice over next year's payout, taken here as next year's earnings
What it says in wordsWhen the cost of equity falls by a quarter point and growth holds, the multiple rises from 20 to about 21.05, a 5.3% gain.

So the equity gain is Rs 500 crore times 5.26%, about Rs 26.3 crore. The straight-line duration shortcut gives 20 times 0.25%, 5%, or Rs 25 crore; the exact figure is higher because of convexity, which is large for anything with a duration of 20.

What the 50 basis point cut does to each sleeve, Rs crore+6.0Bonds, Rs 300 crduration 5+26.3Equities, Rs 500 crduration 2032.3Total gainWhy equities gain moreBondsyield falls 0.40%x duration 5 = 2.0%Equitiescost of equity falls 0.25%x duration 1/(r-g) = 20= 5.0% straight line,5.26% exactonly if growth holds at 6%
The 50 basis point cut lifts Kaushiki's bonds by Rs 6.0 crore and its equities by Rs 26.3 crore, a total of Rs 32.3 crore, because equities priced at 20 times earnings have a duration of about 20 against 5 for the bonds.
Step 3What could make the equity estimate wrong?

The reason for the cut. A central bank that cuts because inflation is falling helps equities; one that cuts because the economy is weakening is also telling you growth may slow. If growth slips from 6.00% to 5.75% at the same time, r minus g is unchanged at 5%, and the equity gain is zero; if it slips to 5.50%, equities lose about Rs 24 crore. The bonds gain Rs 6 crore in every case, which is why bonds are the more reliable beneficiary of a cut even though equities can gain more.

The equity gain depends on why the central bank cutGrowth holds at 6.00%+26.3Growth slips to 5.75%0.0Growth slips to 5.50%-23.80Rs crore, equity sleeve
The equity sleeve gains Rs 26.3 crore if growth holds at 6%, nothing if growth slips a quarter point, and loses Rs 23.8 crore if growth slips half a point, while the bonds gain Rs 6.0 crore in every case.

Where candidates lose it

The common slip is answering that bonds gain and equities gain a little, without a number for equities. The duration of equity, 1 over r minus g, is the tool the question is testing, and at 20 times earnings it is four times the bond duration.

The second is forgetting that growth sits in the same denominator as the discount rate. A cut that comes with weaker growth can leave equities flat or lower, and interviewers probe that straight away.

What the interviewer asks next

  • What if the market were at 12 times earnings instead of 20? Which sleeve gains more then?
  • The bond yields fall only 10 basis points because the cut was fully expected. What changes?
  • How would a rate cut affect bank stocks differently from the broad market?
  • Why might the rupee weaken after a cut, and how would that affect a fund with foreign holdings?

Asked at PIMCO, Product & Strategy, Los Angeles, 2024 (Wall Street Oasis): had only one 'technical' question about the effect of a rate cut on equity prices

Company names and figures are illustrative.