Duration Positioning Before a Policy Rate Rise
A pension scheme has PKR 800 million invested in a ladder of Pakistan Investment Bonds. The portfolio’s modified duration is 6.8 years, and the yield is 11.5%. The scheme’s actuary reports that the present value of three-year liabilities is highly sensitive to the same yield curve. At the next monetary policy announcement the SBP is widely expected to raise the policy rate by 75 basis points, and the scheme’s investment committee wants to act before the meeting. The committee is debating switching 50% of the portfolio into 6-month T-bills, holding cash, or buying longer-dated PIBs to pick up yield. Transaction costs in PIBs are estimated at 0.25% of traded value; T-bills are more liquid. The scheme cannot use derivatives. The actuary warns that liability discount rates will also move with yields, but not one-for-one.
1. Estimate the mark-to-market impact of a 75 bp parallel rise on the current portfolio, stating the duration approximation and its limitations.
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Using modified duration, the approximate percentage price change is −D × Δy / (1 + y), or −6.8 × 0.0075 / 1.115 = −4.57%. On PKR 800m that is a mark-to-market loss of about PKR 36.6m. A simpler first-order approximation, −D × Δy, gives −5.1%, or PKR 40.8m, but it overstates the loss because it ignores the yield denominator.
The estimate assumes a parallel shift, no change in credit or liquidity spreads, and no convexity effect. Convexity would reduce the loss slightly. A real curve shift may be non-parallel, and PIB market prices may move by more than the model if liquidity dries up. The liability side also matters: if discount rates rise, the present value of the three-year liabilities falls, partly offsetting the asset loss, but not one-for-one.
2. Evaluate the three proposed moves against the liability objective and recommend a rebalancing, with calculations for a duration target of 3.5 years.
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Buying longer PIBs increases duration and would amplify the loss if the rate rise occurs; it is a yield-seeking move, not a liability-hedging move. Holding cash reduces duration but creates reinvestment risk and may not match three-year liabilities. Switching 50% into six-month T-bills would reduce duration sharply: if T-bill duration is about 0.5, new duration = 0.5 × 6.8 + 0.5 × 0.5 = 3.65 years, close to the 3.5 target. A precise target requires shifting x to T-bills: 6.8 − x(6.8 − 0.5) = 3.5, so x = 3.3 / 6.3 = 52.4%, or about PKR 419m. Transaction cost on the PIB sale is about 0.25% × 419m = PKR 1.05m.
Recommendation: do not make a binary rates bet. Shift part of the portfolio toward 3-year PIBs and T-bills to bring duration closer to the liability horizon, retain some longer PIBs for yield, and stage the trades to limit market impact. The committee should document that the actuary’s discount-rate offset is uncertain.