Direct answer
A “worked example of rate cuts” is a step-by-step numerical scenario that shows how a central bank lowering its policy interest rate could influence interest rates, bond prices, and borrowing costs—assuming a set of explicit inputs. Because real markets react to expectations, not only to the announced cut, any example must state assumptions and limitations.
Mechanism or definition
A rate cut usually refers to a central bank reducing a policy rate (the rate it uses as a benchmark tool). The intended transmission is generally:
- the cut lowers short-term interest rates referenced to or influenced by the policy rate;
- that can change longer-term yields (after expectations and risk premia adjust);
- changed yields can affect asset pricing (for example, bond prices) and the cost of borrowing.
A key distinction: stable mechanics versus variable conditions.
- Stable mechanics you can illustrate with basic math (e.g., present value for a bond).
- Variable conditions you cannot assume away (e.g., how much the market already expected the cut, how inflation expectations behave, credit risk changes, or execution costs).
Evidence or example (fully specified numerical scenario)
Below is one self-contained scenario. It is not a prediction of real outcomes; it is a demonstration of how rate cuts can propagate through pricing.
Assumptions (state these before calculating)
- Consider a zero-coupon bond (a bond with a single payment at maturity). This simplifies the math.
- Maturity: 1 year.
- Face value at maturity: 100 (currency units).
- Before the cut, the relevant discount rate is 5% per year.
- After the cut, the discount rate becomes 4% per year.
- Ignore taxes, default/credit risk, and liquidity effects.
- The only change is the discount rate; the maturity, payoff, and other parameters stay constant.
Step-by-step calculation
A zero-coupon bond price using discounting is:
- Price = Face / (1 + r)
Before the cut:
- r₀ = 0.05
- Price₀ = 100 / (1 + 0.05) = 100 / 1.05 ≈ 95.24
After the cut:
- r₁ = 0.04
- Price₁ = 100 / (1 + 0.04) = 100 / 1.04 ≈ 96.15
Implied price change:
- ΔPrice = 96.15 − 95.24 ≈ +0.91 (about +0.96% relative to 95.24)
What this example is showing
- In this simplified setting, lowering the discount rate increases the present value of a fixed future payoff.
- In real markets, the “r” you should use is not always equal to the policy rate; it also reflects expectations and risk premia.
Limitations and risks (material failure modes)
- Expectation effects can dominate. If markets already priced in the cut, the actual repricing may be smaller (or occur before the decision). Your calculation changes only the discount rate by assumption.
- Transmission is not immediate. Pass-through from policy rate to market yields and then to borrowing costs can involve delays.
- Risk and liquidity are ignored. In the example, we assumed away default risk, bid-ask spreads, and liquidity changes. In practice, rate cuts can coincide with changing credit conditions.
- Model choice matters. Bond pricing might use more complex term structures than a single constant discount rate.
- Non-stationary relationships. Even if a past episode showed certain patterns, that does not guarantee similar dynamics later.
Verification or next question
To independently verify the “rate cut” story mechanics, you can compare:
- the central bank’s policy rate decision dates (confirm what changed);
- the movement in short-term and relevant longer-term interest rates/yields around that time;
- whether the market appeared to expect the cut beforehand (e.g., using pre-announcement expectations data if available);
- macro context (inflation trend, growth indicators) that could explain why yields moved.
A useful next question is: which interest rate is the right “r” for the asset you care about (policy rate, money-market rate, a specific benchmark yield, or a forward/term-structure measure), because the worked example’s outcome depends entirely on that mapping.