Roll down

On a normal, upward-sloping yield curve, longer bonds yield more than shorter ones. A ten-year bond might yield 8% while a five-year bond yields 6%.

Now simply wait. Five years pass, and the ten-year bond is a five-year bond. If the curve has not moved, it no longer yields 8% — it yields whatever five-year paper yields, which is 6%.

A lower yield means a higher price. So the bond has gained value for no reason other than the calendar.

That is roll down. The bond rolls down the curve towards the short end, and the price rises as it goes.

The holder collects twice: the coupons along the way, which are cash in hand, and the price appreciation on top.

None of this needs interest rates to change. It needs the curve to keep sloping upwards and time to pass.

The workbook's statement (Chapter 19, section 19.3.1). In a typical rising yield curve, as one progresses with time the remaining yield to maturity declines. Its worked illustration: you buy a 10-year bond for an 8% yield, and after 5 years, when the remaining maturity is just 5 years, the yield is say 6%. The value of the bond appreciates. So the portfolio takes advantage of both the coupon payments — cash in hand — and the price appreciation of the bond.

Why the yield falls without the market moving. The bond has not changed, but its place on the curve has. It is now priced off the 5-year point of the curve rather than the 10-year point. On an upward-sloping curve that point carries a lower yield, and a lower yield on a fixed set of remaining cash flows means a higher price.

What the strategy depends on. Two things, and neither is a forecast of rate direction:

1. the yield curve must be upward sloping — the workbook's condition is a typical rising yield curve;
2. time must pass, with the curve broadly holding its shape.

Where it sits. Roll down is one of the active interest-rate strategies in section 19.3.1, listed with a barbell of short and long duration bonds, zero coupon bonds, floaters, maturity extension and buying convexity. The chapter's framing is that all of these depend on the interest rate structure across maturities — the yield curve — and on the manager's view of its three S's: shift, slope and shape.

The two figures the workbook gives are the ones in its own illustration: a 10-year bond bought at 8%, and a 5%-remaining-maturity yield of 6% five years later. It attaches no rupee amounts and no measured roll-down return.

Applying the workbook's own illustration with rupee amounts. A portfolio manager buys Rs 5,00,00,000 face value of a 10-year government security with an 8% coupon at par, so the yield is 8%.

The curve is upward sloping and, for this illustration, stays exactly where it is.

Coupons. At 8% on Rs 5 crore, she collects Rs 40,00,000 a year. Over five years that is Rs 2,00,00,000 in cash.

Roll down. After five years the bond has five years left and is priced off the 5-year point of the curve, at 6%. An 8% coupon bond yielding 6% with five annual coupons left is worth roughly:

• discount the five Rs 40,00,000 coupons and the Rs 5,00,00,000 principal at 6%
• price works out to about Rs 5,42,00,000, that is about Rs 108.40 per Rs 100 face

So the holding has appreciated about Rs 42,00,000 on top of the Rs 2,00,00,000 of coupons — a gain of roughly 8.4% of face value, delivered by nothing but the passage of time on an unchanged curve.

What can take it away. If over those five years the whole curve had shifted up by 2%, so that 5-year paper now yields 8% instead of 6%, the bond would be back at par and the Rs 42,00,000 would not exist. Roll down is a gain from the slope of the curve; a shift in the curve can cancel it.

Chapter 19 (Fixed Income Portfolio Management Strategies), section 19.3.1, sets out roll down among the active interest rate strategies, with the 10-year-at-8%-becoming-5-year-at-6% illustration.

Expect a conceptual question on what a roll-down strategy needs (an upward-sloping yield curve), on the two sources of return (coupon plus price appreciation), or one that asks which strategy profits purely from the passage of time. The strategy is also examined as part of the list — candidates are asked to identify which of several named approaches is an active interest-rate strategy.

• Roll down needs an upward-sloping curve. On a flat curve there is nothing to roll down to, and on an inverted curve the effect runs the other way.
• It is not a rate forecast. The gain comes from the slope and from time, not from a view that yields will fall.
• The return has two parts. Coupons and price appreciation. Answering with only the coupon misses the point of the strategy.
• A shift in the curve can wipe it out. Roll down assumes the curve holds its shape; a parallel upward shift removes the gain.
• Roll down is not rollover, which is carrying a position or a deposit forward into a new period, and it is not roll yield, which is the commodity futures gain or loss from rolling between contract months. Three different ideas that share a word.
• Do not confuse it with maturity extension, the strategy immediately before it in the same section — that buys long-dated bonds for their higher yield and accepts high duration risk, rather than harvesting the slope over time.