Why a Convertible Bond Can Fall When Its Stock Rises: The Conversion Premium

A hypothetical convertible falls 3.2% while its underlying stock rises 10%. With the conversion ratio unchanged, those prices imply that the conversion premium has fallen from 25% to 10%. This describes the relationship between the two prices; explaining why the bond was repriced still requires information about its terms and the market.

The useful question is therefore more precise than “Am I bullish on the stock?” It is: how much of the bond’s purchase price is supported by current conversion value, and what premium must still be present when I sell? The distinction matters most when a seemingly modest move in the stock is being used to justify a much larger price paid for the convertible.

Start with the shares, not the bond’s face value

For a conventional fixed-ratio convertible, let F be face value, K the contractual conversion price and S the current share price. The conversion ratio is q = F ÷ K. Conversion value, also called parity, is V = q × S. Using bond price B on a consistent monetary basis, the market conversion premium is p = B ÷ V − 1.

Consider a hypothetical bond with face value 100 and a fixed conversion price of 20. It represents five shares. With the stock at 24, conversion value is 120. A bond price of 150 therefore carries a 25% premium to conversion value: 150 ÷ 120 − 1. The 50% excess over face value is a different number and answers a different question.

Nor is the contractual conversion price of 20 the investor’s effective stock acquisition cost after paying 150 for the bond. Dividing that purchase price by five gives 30 per share. The conversion price determines the share count; under the assumed terms it is not an additional cash exercise payment. Immediately exchanging the purchased bond for five shares worth 120 would give up 30 of value, or 20% of the 150 outlay, before costs. A 25% premium over parity is not a 25% loss measured against purchase cost.

These numbers are an original illustration, not a quoted security. The two valuation snapshots use the same currency and unchanged conversion terms. The example has no coupon accrual, coupon payment, dividend, tax, transaction cost or currency movement between snapshots. Prices are monetary amounts per 100 face value. It is a comparison before any redemption or conversion event, not an assumed maturity payoff.

Pair stock-price scenarios with ending conversion premiums

Suppose the stock rises from 24 to 26.40. Five shares are then worth 132. If the bond still trades at a 25% conversion premium, its price is 165, matching the stock’s 10% gain in this particular scenario. If the ending premium is instead 10%, the bond is worth 132 × 1.10 = 145.20. Relative to the 150 purchase price, that is a loss of 4.80, or 3.2%.

The matrix varies both inputs. Every cell shows the ending bond price, followed by its price return from 150. The column headings are ending conversion premiums, not bond returns. Each cell is a separate conditional quote scenario; the table does not assign probabilities or estimate fair prices.

Reading across the 26.40 row shows why a correct view on equity direction can still produce very different bond results. Reading down the 10% premium column shows how much stock appreciation is needed to overcome the initial premium. Even a 20% stock gain leaves a 4% bond loss if the ending premium is zero. Conversely, the upper-right cell gives a small bond gain despite a stock decline because it assumes a much larger ending premium; that is a condition, not a claim that premiums will cushion falling markets.

The break-even premium is a decision threshold

With a fixed conversion ratio, the exact price-return identity is:

1 + bond price return = (1 + stock price return) × (1 + ending premium) ÷ (1 + starting premium).

For the 10% stock gain and 25% starting premium, setting the bond return to zero gives an ending premium of 1.25 ÷ 1.10 − 1 = 13.6364%. The premium can fall by about 11.36 percentage points from 25% before the bond’s gross price gain disappears. A 10% ending premium is below that threshold, so the bond loses money in the illustration.

The equation can be reversed. If the ending premium is assumed to be 10%, the stock must reach 150 ÷ (5 × 1.10) = 27.2727 to support the original bond price. That is a 13.6364% stock gain from 24. If the ending premium is zero, the required stock price is 30, a 25% gain. Neither result predicts where the stock or premium will go; each states what would have to be true for price break-even.

Do not subtract percentage points from the stock return

A premium falling from 25% to 10% is a decline of 15 percentage points. It does not mean that the bond loses 15% before adding the stock’s 10% gain. The relevant multiplier changes from 1.25 to 1.10, a 12% reduction. Combining it with the stock move gives 1.10 × 0.88 − 1 = −3.2%.

An amount-based check reaches the same answer. First mark the five-share conversion value from 120 to 132 while retaining the old 25% premium: the bond rises from 150 to 165. Then apply the new 10% premium to the new conversion value: the price falls by 19.80 to 145.20. The net change is 15 − 19.80 = −4.80. That staged attribution is order-dependent, but the final price and the multiplicative identity are not.

A conversion premium is an observed ratio, not a pricing engine

The matrix explains how two quoted prices fit together. It does not prove that the premium is an independent cause of every bond move. Premium is calculated from the bond and stock prices themselves. It can compress simply because conversion value rises faster than the bond; identifying why the bond was repriced requires additional information about the instrument and the market.

Time remaining, conversion restrictions and the issuer’s credit position cannot be recovered from the premium alone. Holding the premium fixed in a table is also not an estimate of the bond’s actual equity sensitivity. The identity contains no volatility model, credit valuation or forecast of investor demand. It should not be presented as any of those things.

For the same reason, the convertible with the lowest premium is not automatically the cheapest security. A comparison needs compatible conversion rights, remaining terms, issuer risk, currency and executable prices. A low or negative displayed premium is a prompt to check the data and terms, not proof of a profit that can be locked in by converting and selling shares.

Move from displayed prices to an investor’s cash result

Use bond and stock observations from the same time, confirm the effective conversion price and check whether the bond quote includes accrued interest. A changed conversion ratio invalidates the fixed-five-share return identity. Stock-price adjustment conventions, delayed last trades and bid–ask spreads can also make a screen comparison misleading. A conversion value is not a promise that shares can be obtained and sold instantly at that value.

The table excludes costs. Adding an entry charge of 0.50 and an exit charge of 0.50 to the 150-to-145.20 scenario changes the cash return to (145.20 − 0.50) ÷ (150 + 0.50) − 1 = −3.85%, rounded. With those charges, the gross sale price must reach 151 to recover the 150.50 entry outlay after the 0.50 exit cost. At a stock price of 26.40, that requires an ending conversion premium of about 14.3939%, rather than the cost-free 13.6364%. For an interest-paying bond, use actual accrued interest at each settlement and add coupons received once. Price return and total return then need not match, which is also central to distinguishing a quoted bond yield from an investor’s holding-period return.

A practical comparison finishes with three explicit inputs: the actual purchase outlay, the share value implied by the current conversion terms, and a range of possible exit premiums. The stock view supplies only one of them. The break-even calculation makes the missing assumption visible before a price target on the equity is mistaken for a return target on the convertible.