This note is my own reference for a very specific question:

“I have sold down a chunk of my equity book. Inflation is high. I do not want the cash sitting at 0%, but I also want to be able to redeploy into stocks in ~2 months. Should I park the money in long gilts (IGLT / 7–10y Treasuries), or in ultra-short bonds / cash-like instruments?”

Intuitively, gilts “pay a yield”, so it is tempting to think:

“Inflation is ~4%, this gilt fund yields ~4–5%, so I am protected.”

The problem is duration. If you use long duration bonds as a temporary parking lot, you are not “earning yield”. You are making a leveraged macro bet on interest rates with your dry powder.

This post is my attempt to write down:

  1. The problem: parked cash vs inflation vs equity optionality.
  2. The maths: how bond prices respond to yield moves via duration.
  3. Why short duration is better than long for this 2-month problem.
  4. Extra context: inflation vs interest-rate risk, and when long bonds do make sense.

1. The Problem: Cash, Inflation, and Optionality

Setup:

  • I am willing to sit out of equities for a while.
  • I want that capital to be ready to pounce when valuations get interesting.
  • I do not want it sitting in a 0% current account while UK inflation runs around a few percent.
  • My expected redeployment window is ~2 months, but I may act sooner if something compelling shows up.

So the capital has three jobs at once:

  1. Keep nominal value roughly intact (no equity-like drawdowns).
  2. Earn something non-trivial vs leaving it idle at 0%.
  3. Stay highly liquid so I can buy stocks the day I want to.

For that problem, the relevant question is not:

“Which bond has the highest yield?”

but:

“How much price volatility am I taking on for that yield, over a 2-month window?”

That is exactly what duration measures.

2. From Coupons to Yields to Prices

Take a plain fixed-rate bond with face value $F$ and annual coupon rate $c$. It pays $cF$ per year and returns $F$ at maturity.

Let:

  • $y$ – yield to maturity (YTM), per year, in decimals.
  • $n$ – number of years to maturity.
  • Cash flows: $CF_t = cF$ for $t = 1, 2, \dots, n-1$, and $CF_n = cF + F$.

The standard pricing formula is:

\[P(y) = \sum_{t=1}^{n} \frac{CF_t}{(1 + y)^t}\]

Two important points:

  1. The coupon rate $c$ is fixed by the issuer at issuance.
  2. The yield $y$ is an output of the current market price $P$.

If the market demands a higher required return:

  • Yields “go up” from 4% to 5%.
  • Prices fall to a new level where the same fixed coupons now imply a 5% YTM.

This is all “gilt yields went up” really means: required returns on those cashflows rose, so prices adjusted down.

3. Duration: Turning “Years” into Price Sensitivity

Duration is the bridge between “yield moves” and “price moves”.

3.1 Macaulay duration

First define the PV weight of each cash flow:

\[w_t = \frac{\dfrac{CF_t}{(1 + y)^t}}{P(y)}.\]

These weights sum to 1. Macaulay duration is:

\[D_{\text{Mac}} = \sum_{t=1}^{n} t \cdot w_t.\]

Interpretation:

$D_{\text{Mac}}$ is the PV-weighted average time (in years) at which you receive the bond’s cashflows.

For a long gilt with final maturity 15+ years away, $D_{\text{Mac}}$ might be ~11–12 years. For a 6-month bill, it is ~0.5.

3.2 Modified duration

For price sensitivity we use modified duration:

\[D_{\text{mod}} = \frac{D_{\text{Mac}}}{1 + y}.\]

Differentiating the price with respect to yield gives:

\[\frac{dP}{dy} = -D_{\text{mod}} \cdot P.\]

Divide by $P$:

\[\frac{1}{P}\frac{dP}{dy} = -D_{\text{mod}}.\]

For a small change in yield $\Delta y$:

\[\frac{\Delta P}{P} \approx -D_{\text{mod}} \cdot \Delta y.\]

This is the core approximation:

Rule: percentage price change $\approx -(\text{modified duration}) \times (\text{change in yield})$.

So if:

  • $D_{\text{mod}} = 7.6$
  • $\Delta y = +0.01$ (yields up 1 percentage point)

then:

\[\frac{\Delta P}{P} \approx -7.6 \times 0.01 = -0.076 = -7.6\%.\]

i.e. a 1% rise in yields → ~7.6% drop in price.

4. A Concrete Long-Gilt Example

Consider a 10-year gilt with:

  • Face $F = 100$,
  • Coupon rate $c = 4\%$,
  • Yield $y = 4\%$.

At 4% yield, the bond is worth essentially par:

\[P(4\%) \approx 100.\]

Now reprice at $y = 5\%$. The same $4$ coupon on a 100 face is now less attractive, so the bond trades below par.

If you plug the cashflows into the pricing formula (or a quick script), you get approximately:

  • $P(4\%) \approx 100$
  • $P(5\%) \approx 92.28$

The percentage change is:

\[\frac{92.28 - 100}{100} \approx -7.72\%.\]

which is exactly what the duration rule is telling us:

  • Here, $D_{\text{mod}} \approx 7.7$,
  • $\Delta y = +0.01$,
  • So $\Delta P / P \approx -7.7\%$.

In other words:

A 1% move up in yields on this longish bond wipes out roughly 1.7 years of coupon income in one shot.

For a broad gilt ETF with effective duration ~7–8, this is the same story, just aggregated across many bonds.

5. An Ultra-Short Example: Same Yield Move, Tiny Pain

Now contrast this with a 6-month instrument.

Suppose you have a 6-month bill with a simple annualised yield of 4%. For intuition, model it as:

  • Face $F = 100$,
  • Maturity in $T = 0.5$ years,
  • Price at 4% is basically:
\[P_{4\%} \approx \frac{100}{1 + 0.04 \cdot 0.5} = \frac{100}{1.02} \approx 98.04.\]

Now yields move to 5%:

\[P_{5\%} \approx \frac{100}{1 + 0.05 \cdot 0.5} = \frac{100}{1.025} \approx 97.56.\]

Percentage change:

\[\frac{97.56 - 98.04}{98.04} \approx -0.49\%.\]

So for the same 1% move in yields:

  • 10-year 4% bond: ~–7.7% price hit.
  • 6-month bill: ~–0.5% price hit.

Same maths. The only difference is duration:

  • Long bond: lots of cashflows far in the future → high duration.
  • 6-month bill: everything comes back soon → low duration.

In the ultra-short case, the market does not need to punish the price much because:

“You are getting your money back in a few months anyway; you will then be able to reinvest at the new higher yield.”

6. Why This Matters for a 2-Month Parking Problem

Go back to the original problem:

  • Horizon: about 2 months, but with the option to redeploy into equities any day.
  • Objective: “Do not sit at 0% while inflation is high, but keep dry powder intact.”

Two key observations:

  1. Over 2 months, even 4% annual inflation only erodes:

    \[0.04 \times \frac{2}{12} \approx 0.67\%.\]

    So the real loss from doing nothing is on the order of two-thirds of a percent.

  2. Long duration gilts can easily swing ±2–5% in a random 2-month window, simply from rate noise.

So in this context, the risk trade-off is:

  • Inflation risk over 2 months: ~0.7% real erosion if you literally earn 0%.
  • Duration risk on long gilts: a small change in the rate narrative (higher-for-longer, fiscal worries, curve repricing) can cost you several percent.

If the goal is “parked cash that may be needed quickly”, then:

  • A long gilt ETF is not a cash substitute; it is a macro trade.
  • The extra yield you are chasing over 2 months (~0.7–0.9% of coupon accrual) is small relative to the downside tail from duration.

6.1 What ultra-short gives you instead

Ultra-short bond funds (or money-market ETFs):

  • Own bonds with maturities mostly under 1 year.
  • Have effective duration often in the 0.1–0.5 range.
  • Still pay a yield that tracks short-term interest rates reasonably closely.

So if yields move by 1%:

\[\frac{\Delta P}{P} \approx -D_{\text{mod}} \Delta y.\]
  • With $D_{\text{mod}} \approx 0.25$, you are looking at ~–0.25% price impact.
  • At the same time, the fund is constantly rolling into new issues at the new, higher yields, so your income adjusts quickly.

That is exactly what you want from a 2-month parking instrument:

  • Small price wiggles.
  • Reasonable yield.
  • Quick reset when the rate environment changes.

7. Inflation Hedge vs Rate Bet vs Crash Hedge

One more distinction that is easy to blur:

  1. Inflation hedge (real purchasing power) – in the UK context, this is closer to index-linked gilts and real assets. They explicitly link cashflows to an inflation index, but can still be volatile because real yields move.
  2. Rate bet / duration trade – long conventional gilts or 7–10y Treasuries are mostly this:
    • If we move into a recession / cuts regime → yields fall → bonds rally.
    • If we move into “higher for longer” → yields rise → bonds sell off.
  3. Crash hedge vs equities – long duration government bonds tend to perform well in “growth scare” or deflationary shocks, and badly in inflation shocks.

For the 2-month parking problem, the priority is not a deep inflation hedge or a big macro view. It is simply:

“Do not lose real money while I wait, and do not blow up my optionality.”

That pushes you naturally towards:

  • Cash / high-yield savings accounts, or
  • Ultra-short / money-market funds in your brokerage account.

Long gilts sit in a different mental bucket: explicit macro trade, not “cash with yield”.

8. Summary

The key mathematical object is modified duration:

\[\frac{\Delta P}{P} \approx -D_{\text{mod}} \cdot \Delta y.\]
  • Long gilt portfolio: $D_{\text{mod}} \approx 7$–$8$ → 1% move in yields ≈ 7–8% price move.
  • Ultra-short bond portfolio: $D_{\text{mod}} \approx 0.1$–$0.5$ → 1% move in yields ≈ 0.1–0.5% price move.

For parked cash over 2 months, the inflation erosion is modest. The bigger danger is accidentally turning your dry powder into a levered bet on the yield curve.

So the logic stack I am using is:

  1. Over short horizons, minimise duration, not boredom.
  2. Treat long bonds as a separate, deliberate macro position, not as “cash with yield”.
  3. If I want a place to sit while waiting for equity opportunities, I will take:
    • A cash / savings account or
    • An ultra-short bond / money-market ETF, before I reach for IGLT / 7–10y Treasury ETFs.

Appendix – Duration Derivation (Sketch)

For completeness, here is the calculus behind the duration rule.

Start from the price:

\[P(y) = \sum_{t=1}^{n} \frac{CF_t}{(1 + y)^t}.\]

Differentiate w.r.t. $y$:

\[\frac{dP}{dy} = \sum_{t=1}^{n} CF_t \cdot \frac{d}{dy}\left[(1 + y)^{-t}\right] = \sum_{t=1}^{n} CF_t \cdot \left[-t(1 + y)^{-t-1}\right].\]

Factor out $(1 + y)^{-1}$:

\[\frac{dP}{dy} = -\frac{1}{1 + y} \sum_{t=1}^{n} t \cdot CF_t (1 + y)^{-t}.\]

Now divide and multiply by $P$:

\[\frac{dP}{dy} = -\frac{P}{1 + y} \cdot \frac{\sum_{t=1}^{n} t \cdot \dfrac{CF_t}{(1 + y)^t}}{\sum_{t=1}^{n} \dfrac{CF_t}{(1 + y)^t}}.\]

The fraction is exactly the Macaulay duration:

\[D_{\text{Mac}} = \frac{\sum_{t=1}^{n} t \cdot \dfrac{CF_t}{(1 + y)^t}}{\sum_{t=1}^{n} \dfrac{CF_t}{(1 + y)^t}}.\]

So:

\[\frac{dP}{dy} = -\frac{P}{1 + y} D_{\text{Mac}} = -D_{\text{mod}} \cdot P.\]

with:

\[D_{\text{mod}} = \frac{D_{\text{Mac}}}{1 + y}.\]

Then for small $\Delta y$:

\[\Delta P \approx \frac{dP}{dy}\Delta y = -D_{\text{mod}} P \Delta y.\]

This is the “1% up in yields → –7.6% in price” relationship I keep referring back to.