Case 020Fixed income and cash managementHard

A client with a Rs 5 crore debt sleeve expects rates to fall 1 point. Compare a 1-year duration fund with an 8-year duration gilt fund if rates fall 1 point, and if they instead rise 0.5 point.

The situation

Padmini Rao-Nambiar, 51, holds Rs 5 crore of her portfolio in debt. She reads that the central bank may cut rates by a full point over the next year and asks whether to move the sleeve from its short-term fund into a long gilt fund.

The 1-year fund yields 6.9% after costs with a modified duration of 1 and negligible convexity. The gilt fund yields 7.2% after costs with a modified duration of 8 and convexity of about 80. Assume the yield move happens at the start of the year and both funds then earn their yield for the year. All figures are illustrative.

Your task

Work out the one-year return in per cent and rupees for both funds under both moves, find where they break even, and say how you would size the bet.

Quick check

If yields rise 0.5 point instead of falling, roughly what does the 8-year gilt fund return over the year?

Worked solution

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

30-second answerThe answer to give first

If rates fall 1 point, the gilt fund earns about 15.6%, Rs 78 lakh, against 7.9% on the short fund; if they rise 0.5 point, it earns 3.3% against 6.4%. The gilt fund wins only if yields rise less than about 4 basis points. That is a genuine bet on her view, so size it: moving half the sleeve keeps the wrong case acceptable.

Step 1How does a rate move turn into a return?

Think of a see-saw with the yield on one end and the bond price on the other; duration is how far the price end sits from the pivot. A bond fund's price moves by about minus its duration times the change in yield, and over a year it also earns its yield, so one-year return is roughly yield minus duration times the move, plus a small convexity term. For the gilt fund, a 1 point fall gives 8% of price gain and 0.4% from convexityThe curve in the price-yield relationship: prices rise a little more when yields fall than they drop when yields rise by the same amount., plus 7.2% of yield: 15.6%. For the 1-year fund the same fall adds only about 1%.

The relationship
R≈y−D Δy+12C (Δy)27.2−8(−1.0)+12(80)(0.01)2×100=15.6%R \approx y - D\,\Delta y + \tfrac{1}{2} C\,(\Delta y)^2 \qquad 7.2 - 8(-1.0) + \tfrac{1}{2}(80)(0.01)^2 \times 100 = 15.6\%
ythe fund's yield after costs, earned over the year
Dmodified duration, the price sensitivity to yield
Δychange in yield, here -1 point
Cconvexity, the curve's correction
What it says in wordsOne-year return is the yield earned plus the price change from the rate move, which duration sizes and convexity slightly improves.
Same Rs 5 crore, two funds, two rate moves: rupees earned in a yearIf rates fall 1 pointRs 39.5 lakh1-year fund7.91%Rs 78.0 lakh8-year gilt fund15.60%If rates rise 0.5 pointRs 32.0 lakh1-year fund6.40%Rs 16.5 lakh8-year gilt fund3.30%
On Rs 5 crore, a 1 point fall earns Rs 78.0 lakh in the gilt fund against Rs 39.5 lakh in the 1-year fund, while a 0.5 point rise earns Rs 16.5 lakh against Rs 32.0 lakh.
Step 2Where do the two funds break even?

Set the two returns equal. The gilt fund starts 0.3 points ahead on yield but loses about 7 points more for every point yields rise. The lines cross at a rise of only about 4 basis points, so the gilt fund is a bet that yields fall or stay put, not a bet that pays off in most outcomes. It still earns a positive 3.3% in the 0.5 point rise; the cost of being wrong is Rs 15.5 lakh of return given up, not a loss of capital. A larger rise changes that: at +1.5 points the gilt fund returns about -3.9%.

The gilt fund wins only if yields do not rise more than a few basis points-5%0%5%10%15%20%-1.5-1.0-0.50+0.5+1.0+1.5Change in yields over the year, percentage pointsCross at +4 bpCut: 15.6%Rise: 3.3%8-year gilt fund1-year fund
The 1-year fund's return barely moves with yields, while the 8-year gilt fund's return swings from about 20.1% to -3.9% across a 1.5 point fall or rise, and the two cross at a rise of only about 4 basis points.
Step 3How would you size the bet?

Size it so the wrong outcome is one she can live with, the way you would only lend a friend what you can afford not to see again. Moving half the sleeve, Rs 2.5 crore, into the gilt fund gives a blended duration of about 4.5: roughly Rs 59 lakh if rates fall a point and Rs 24 lakh if they rise half a point. The view gets expressed, and a surprise costs her about Rs 7.8 lakh of return rather than twice that. Ask also what the debt sleeve is for. If it is the part of her wealth meant to stay steady while equity swings, a duration bet makes it behave more like the risky part.

Say the limits. Rate cuts that are widely expected are often already in long bond yields, so the cut she reads about may move them less than a point. Duration and convexity describe small parallel moves; real yield curves twist. And both funds are taxed the same way here, so tax does not change the ranking.

Where candidates lose it

The usual slip is quoting only the price change, +8% or -4%, and forgetting that both funds earn their yield over the year. That makes the gilt fund look like it loses money in a 0.5 point rise, when it actually earns 3.3%, just far less than the short fund.

The second miss is treating the client's view as a forecast to act on in full. Interviewers want the breakeven, a few basis points, and a sized position that survives being wrong.

What the interviewer asks next

  • The cut is already in the yield curve. What happens to the gilt fund when it is announced?
  • How would a 5-year corporate bond fund at 7.8% with duration 4 fit into this choice?
  • Padmini wants the bet but no chance of a negative year. What is the largest gilt allocation that delivers that if yields rise 1.5 points?

Company names and figures are illustrative.