6B.10 Debt funds · M06B Funds and ETFs

Motivation

A debt fund is a portfolio of bonds marked to market every day, with daily liquidity offered to investors on assets that may take days to sell. That combination produces two risks the bank deposit does not have, interest-rate risk and credit risk, and a third that is specific to the fund structure: the run.

6B.10.1Yield, duration and the NAV#

For a portfolio of bonds $j$ with value weights $w_j$ , the portfolio YTM is the internal rate of return of the combined cash flows (factsheets often show the value-weighted average YTM, which is close for similar maturities). Modified duration $D_j$ and convexity $C_j$ are as in M11 · 11.2–11.3: $D = -\frac{1}{P}\frac{dP}{dy}$ , $C = \frac{1}{P}\frac{d^2P}{dy^2}$ .

Proposition 6B.10.1NAV response to a parallel yield shift

If all yields move by $\Delta y$ , the fund's net assets change by

\begin{aligned} \frac{\Delta \text{NAV}}{\text{NAV}} &\approx -D_p\,\Delta y + \tfrac12 C_p\,(\Delta y)^2,\\ D_p &= \textstyle\sum_j w_jD_j, \quad C_p = \sum_j w_jC_j. \end{aligned} \tag{6B.28}

Over a horizon $h$ (in years) with the shift at the start, the return is approximately

R_h \approx (\text{YTM} - c)\,h - D_p\,\Delta y + \tfrac12 C_p(\Delta y)^2, \tag{6B.29}

and, ignoring convexity, the yield rise that wipes out one year's carry is $\Delta y^* = (\text{YTM} - c)/D_p$ .

Proof

Each bond's price is a smooth function of its yield; Taylor's theorem gives $\Delta P_j/P_j = -D_j\Delta y + \frac12 C_j(\Delta y)^2 + O(\Delta y^3)$ . The fund's net assets are $\sum_j P_j$ times holdings plus cash; dividing the change by the total gives the value-weighted averages (cash has $D = C = 0$ ). Net of expenses, the portfolio accrues approximately its yield less the expense ratio over the horizon if yields then stay put; adding the price change gives (6B.29).∎

Worked example 6B.14

A corporate bond fund with YTM 7.2%, TER 0.6%, $D_p = 3.0$ , $C_p = 12$ : a 1-point rise in yields lowers the NAV by $3.0\% - 0.06\% = 2.94\%$ , and the break-even yield rise over a year is $6.6\%/3.0 = 2.2$ points. A gilt fund with YTM 6.8%, TER 0.5%, $D_p = 9.0$ , $C_p = 110$ : a 1-point rise costs $9.0\% - 0.55\% = 8.45\%$ , and a yield rise of $6.3\%/9.0 = 0.70$ point wipes out a year's carry. A "safe" gilt fund is a duration bet.

Accrual and mark-to-market If yields do not move, a debt fund's NAV rises smoothly at about YTM minus TER (the accrual). When yields move, the NAV moves by (6B.28). Since 1 Apr 2020 all debt and money-market securities are valued at prices from AMFI-appointed independent valuation agencies, not by amortising cost; before that, securities with up to 60 days (from March 2019, 30 days) of residual maturity could be valued by amortisation (SEBI circulars of 22 Mar 2019 and 24 Sep 2019) [S]. Amortisation is a stale price (Proposition 6B.2.1): it does not move when credit news arrives.

Credit risk and side pockets A downgrade or default marks the paper down sharply on the valuation agencies' prices. Since SEBI's circular of 28 Dec 2018 (SEBI/HO/IMD/DF2/CIR/P/2018/160) a scheme may, after a credit event, create a segregated portfolio ("side pocket"): the impaired paper is moved into a separate portfolio, every unitholder on the record date receives units in it one for one, the main portfolio continues to trade at a NAV that excludes the impaired paper, and the segregated portfolio is closed to subscriptions and redemptions and pays out whatever is recovered [S; the 2019 amendment limited segregation of unrated papers to actual defaults]. With total assets $V$ , the impaired paper's current value $X$ and $N$ units, the main NAV is $(V - X)/N$ and each holder also has a claim worth $X/N$ . The side pocket stops the transfer of (6B.4): investors who redeem after the event cannot leave the impaired paper behind for the stayers, and investors who buy after it do not buy a share of a recovery they did not pay for.

6B.10.2Runs and the first-mover advantage#

Proposition 6B.10.2dilution from redemptions when the NAV ignores liquidation costs

A fund with net assets $V$ , $N$ units and fair NAV $v = V/N$ holds no cash, and pays redemptions at $v$ . Raising cash costs a proportion $k$ of the value sold: to pay $R$ it sells securities worth $R/(1 - k)$ . If a fraction $\rho \in [0, 1 - k)$ of units is redeemed, the NAV of the remaining units falls to

v' = v\,\frac{1 - k - \rho}{(1 - k)(1 - \rho)}, \qquad D(\rho) = 1 - \frac{v'}{v} = \frac{\rho\,k}{(1 - k)(1 - \rho)}. \tag{6B.30}

$D$ is increasing and convex in $\rho$ : the more others redeem, the more a stayer loses. If an investor's benefit from staying (expected excess return over the alternative, as a fraction of value) is $b$ , she prefers to redeem when $D(\rho) > b$ , that is when

\rho > \rho^* = \frac{b\,(1 - k)}{k + b\,(1 - k)}. \tag{6B.31}

With swing pricing at $s = k$ , $D(\rho) = 0$ for all $\rho$ .

Proof

Redemptions are $R = \rho Nv$ ; the fund sells $\rho Nv/(1 - k)$ , leaving $Nv[1 - \rho/(1 - k)]$ for $(1 - \rho)N$ units, which is (6B.30) after putting the bracket over $1 - k$ . $dD/d\rho = k/[(1 - k)(1 - \rho)^2] > 0$ and $d^2D/d\rho^2 = 2k/[(1-k)(1-\rho)^3] > 0$ . $D(\rho) > b \iff \rho k > b(1 - k)(1 - \rho) \iff \rho\,[k + b(1 - k)] > b(1 - k)$ , which is (6B.31). The swing-pricing statement is Proposition 6B.2.2.∎

This is the strategic complementarity of Chen, Goldstein and Jiang (2010): each investor's incentive to redeem rises with the number of others who redeem, so beliefs about others' behaviour can become self-fulfilling. If investors expect $\rho > \rho^*$ , all prefer to leave, and a fund holding illiquid assets can be emptied by fear alone. Chen, Goldstein and Jiang found that in US equity funds holding illiquid assets, outflows are more sensitive to poor past performance than in funds holding liquid assets, and that the effect is weaker where large (institutional) investors, who internalise more of the cost, dominate.

Worked example 6B.15

A credit-risk fund with liquidation cost $k = 3\%$ . If 20% of units are redeemed, $D = 0.2 \times 0.03/(0.97 \times 0.8) = 0.77\%$ : the stayers lose 0.77% of their value to the leavers. An investor who expects to earn $b = 0.5\%$ more by staying than by moving her money prefers to redeem once she expects more than $\rho^* = 0.00485/0.03485 = 13.9\%$ of the fund to leave. A cash buffer delays the problem (the first redemptions are paid at no cost) but concentrates the illiquid assets in what remains.

Liquid and overnight funds Overnight funds hold one-day instruments (repo, TREPS); liquid funds hold money-market paper of up to 91 days' maturity. After IL&FS, SEBI's circular of 20 Sep 2019 required liquid funds to hold at least 20% in liquid assets (cash, government securities, T-bills, repo on government securities) and introduced a graded exit load on redemptions within seven days [S]. Both are, in the language of this section, a cash buffer and a swing price.

The backstop Since July 2023, specified debt schemes contribute 25 bp of their AUM (and AMCs a one-time 2 bp) to the Corporate Debt Market Development Fund (CDMDF), which can buy investment-grade corporate debt from contributing schemes in a SEBI-declared market dislocation (SEBI circulars of 27 Jul 2023)¹. It is a lender of last resort for the fund industry's illiquidity, financed by the funds themselves. (The brief for this module mentioned a "debt PCDS framework"; no SEBI framework under that name could be identified on 6 Nov 2026, and nothing is claimed about it here.)

Practitioner notes

Match a debt fund's Macaulay duration to your horizon: then the price change and the reinvestment change roughly offset, and you earn about the starting YTM minus TER (M11 · 11.2).
Read the PRC cell and the monthly portfolio. A short-duration fund with 30% in AA and below paper is a credit fund in disguise.
When a holding is downgraded, look for a side pocket. Redeeming in the days before the markdown is the trade of Worked example 6B.2; the rules exist to deny it to you, and to others at your expense.

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