Conversion Ratio
The number of equity shares received for each convertible security, or the share-exchange rate fixed in a merger. It is fairly priced when the shares receivable are worth exactly what is given up.
In plain language
A convertible bond or convertible preference share lets its holder swap the security for equity shares on a pre-determined date. The conversion ratio says how many shares that swap produces. A ratio of 25:1 means 25 equity shares for every one bond.
The ratio turns two separately traded prices — the bond's and the share's — into one comparison. Multiply the ratio by the share price and you know what the holder would get by converting. When that equals the bond's face value, the workbook calls the conversion ratio fairly priced. When it does not, one of the two securities is mispriced relative to the other, and that is the opening a Category III AIF looks for.
The workbook uses the same idea for mergers: the ratio at which the target's shareholders receive the acquirer's shares lets you compute what either share "should" be worth.
How it works
In convertible arbitrage. A Category III AIF goes long the convertible security and short the same company's equity. The pricing link between them is the conversion ratio. If the share falls, the short position gains while the bond keeps paying coupons; if the share rises, the fund can convert and sell the shares to cover losses on the short.
In merger arbitrage. A full-stock merger announces a conversion ratio. From the target's price and the ratio, a fair price for the acquirer's share can be computed; if the acquirer trades below it, the manager buys.
Chapter 3's summary of Category III strategies names both uses: convertible bonds and shares of the same company can be relatively mispriced in the short term based on the conversion ratio, and mergers help identify mispricing between acquirer and target based on the ratio announced.
The formula
Value of shares on conversion = Conversion ratio × Share price
Fairly priced when: Conversion ratio × Share price = Face value of the convertible
A worked example
The workbook's Fund CAS (Example 6). A 12% convertible bond, face value Rs 1,000, conversion ratio 25:1 after a one-year lock-in. On 1 April 2022 the share is at Rs 40:
25 × Rs 40 = Rs 1,000 = face value → fairly priced
By 31 March 2023 the share is at Rs 42.50 and the bond at Rs 1,050:
25 × Rs 42.50 = Rs 1,062.50 > bond price Rs 1,050 → mispriced
Fund CAS held bonds worth Rs 1 crore (10,000 bonds), financed Rs 20 lakh from its own capital and Rs 80 lakh borrowed at 10%, and was short 50,000 shares. Converting gives 2,50,000 shares:
Coupon + Rs 12,00,000
Borrowing cost − Rs 8,00,000
Borrowing fee on short shares − Rs 2,50,000
Dividend foregone − Rs 1,00,000
Conversion: 2,50,000 × 42.50 − 1,00,00,000 = + Rs 6,25,000
Short squared off at a loss of Rs 2.50/share − Rs 1,25,000
Total + Rs 5,50,000 on Rs 20,00,000 = 27.50%
Illustrative figures. A Tapti Industries convertible debenture of face value Rs 500 converts at 20:1. At a share price of Rs 22, conversion gives 20 × 22 = Rs 440 — less than face value, so conversion is not attractive. At Rs 30, it gives Rs 600.
Why NISM asks about it
Chapter 7, section 7.3 (Convertible Arbitrage Strategy) and section 7.4.2 (Merger Arbitrage Strategy) both turn on the conversion ratio, with worked Examples 6 and 7; Chapter 3 previews both uses. Chapter 7's sample question asks for the strategy that profits from mispricing of a debt security or preference share relative to the equity share. Expect to compute shares receivable and their value, and to judge whether a ratio is fairly priced.
Common exam traps
- Fair pricing compares shares receivable with face value in the workbook's convertible example: 25 × Rs 40 = Rs 1,000.
- The ratio is shares per security, not the security price per share.
- The workbook's merger example contradicts itself. Its text reads "shareholders of Company ID will be issued 139 shares of Company CF, for every 10 shares", yet its fair-price arithmetic — 139 × Rs 39.25 ÷ 10 = Rs 545.58 for Company ID — only works if 139 shares of CF correspond to 10 shares of ID. Its positions table also swaps the two companies' prices. Use the arithmetic: ID at Rs 540 is below Rs 545.58, so ID is under-valued and is bought.
- Borrowing fees and dividends foregone are costs of the short leg; the coupon is income.
- Convertible securities include convertible preference shares, not only bonds.
Check yourself
1.Fund CAS holds a 12 per cent convertible bond of Rs 1 crore face value funded 20 per cent from fund capital and 80 per cent borrowed at 10 per cent, with 50,000 shares sold short at Rs 40 and a borrowing fee of Rs 5 a share. With a 25:1 conversion ratio, a year-end share price of Rs 42.50 and a Rs 2 dividend, its return on investment is:
- a)15.00 per cent
- b)27.50 per cent
- c)5.50 per cent
- d)12.00 per cent
Show the answer
Answer: (b) 27.50 per cent
The items are: borrowing cost (Rs 8,00,000), coupon interest Rs 12,00,000, borrowing fees (Rs 2,50,000), dividend foregone (Rs 1,00,000), profit on conversion of 2,50,000 shares at Rs 42.50 less the Rs 1,00,00,000 investment Rs 6,25,000, and loss on squaring off the short at Rs 2.50 a share (Rs 1,25,000) — a total of Rs 5,50,000 on fund capital of Rs 20,00,000, giving 27.50 per cent. Option (a) is the workbook's alternative outcome: if the price of equity shares had decreased, the fund would not convert and would square off the short, with a net gain of 15 per cent.
2.A merger is announced at a conversion ratio of 139:10. The target trades at Rs 39.25 and the acquirer at Rs 540.00, and both boards and the regulators have approved. What should the fund do?
- a)Short the acquirer, since the acquirer is always shorted in merger arbitrage
- b)Buy both, since the fair price of the acquirer is Rs 545.58 against a market price of Rs 540.00 and deal failure risk is minimal
- c)Buy only the target, since the acquirer's price is irrelevant to the arbitrage
- d)Take no position, since the announcement has already been made public
Show the answer
Answer: (b) Buy both, since the fair price of the acquirer is Rs 545.58 against a market price of Rs 540.00 and deal failure risk is minimal
The fair price of the acquirer implied by the ratio is (139 × Rs 39.25) ÷ 10 = Rs 545.58, against a market price of Rs 540.00, so the equity shares of Company ID are under-valued, based on the conversion ratio offered in the merger transaction, and the investment manager should BUY. And because the merger has already been approved by both the boards and the regulators, the risk of the deal failure is minimal — in such a case, the fund should ideally take long positions in equity shares of the Acquiring Company also. The short in the acquirer is a response to deal-completion uncertainty and an over-valued premium, neither of which applies here. Fund MAS earned 4.86 per cent within one day.
3.Which strategy is used by a Category III AIF to benefit from the mispricing of a debt security or a preference share of a company, in relation to its equity share?
- a)Convertible Arbitrage Strategy
- b)Merger Arbitrage Strategy
- c)Pre-IPO Strategy
- d)Activist Strategy
Show the answer
Answer: (a) Convertible Arbitrage Strategy
This is the workbook's own sample question. Two clues in the stem give it away — a debt security or a preference share points to a convertible or hybrid security, and in relation to its equity share points to the conversion ratio. The fund takes a long position in convertible securities issued by a company and simultaneously takes a short position in the same company's equity shares, to earn a riskless profit, independent of stock price movements. Merger arbitrage involves two different companies, not one company's two securities.
Where this is taught
Free preparation for NISM Series XIX-BRelated terms
- Category III AIFThe AIF category for funds running diverse or complex trading strategies with leverage — hedge funds and their kin — and the only category denied tax pass-through status.
- Convertible debenturesDebentures that turn into equity shares on terms fixed at issue — the investor draws a coupon until conversion, and the company settles the debt in shares instead of cash.
- Preference shareA share carrying a pre-defined rate of dividend, paid before any equity dividend, with priority over equity in return of capital on winding up — but normally no voting rights.
- Convertible bondA bond carrying an embedded option that lets the holder exchange it for a specified number of the issuer's equity shares — a plain bond plus an equity conversion right.
- Convertible ArbitrageA Category III long-short strategy: buy a company's convertible bond or preference share and short its equity, to profit when the conversion terms and the share price fall out of line.
- Merger ArbitrageAn event-driven Category III strategy: go long the target company and long or short the acquirer, to capture the gap between the target's price and the deal price as a merger completes.
- Unaffected share priceA target company's share price before a merger or acquisition is announced — the base over which an acquirer must pay a premium, and the price a merger arbitrageur measures the spread from.
- Automatic Conversion ClauseA clause that forces convertible debt or convertible preference shares to convert into equity when a pre-defined trigger occurs — a revenue level, a funding round or an IPO — unlike an optional conversion right.
- Borrowing feesThe fee a fund pays to borrow securities so that it can take a short position — an additional cost of the short, quite separate from interest on borrowed cash.