Convertible Arbitrage

A convertible security is a bond or preference share that the holder can turn into a fixed number of equity shares on a set date. It pays a coupon like debt, and it rises with the share price like equity.

Because it is part debt and part equity, its price and the share price are linked through the conversion ratio — but the market does not always keep them in line. Convertible arbitrage tries to profit from that.

The fund goes long the convertible and short the same company's equity:

• If the share price falls, the short position gains, and the fund keeps collecting coupons.
• If the share price rises, the fund can convert and sell the shares, offsetting the loss on the short.

The workbook calls it a type of long-short strategy, pursued to earn a profit independent of stock price movements — and in the same breath warns that it is difficult to implement and can be riskier when macro-economic conditions change.

The link (section 10.1.3). Pricing is determined by the conversion ratio. With a ratio of 25:1 on a Rs 1,000 bond, 25 shares at Rs 40 are worth Rs 1,000 — the conversion ratio is fairly priced. If the share rises and the bond does not keep pace, or vice versa, there is a gap to trade.

Cash flows the fund must count:

The workbook's notes to Example 10.6: the borrowing fee is incurred to borrow securities for the short sale; dividends declared do not accrue to a short position; borrowing cost is incurred to the extent of leverage; the coupon is additional income.

What makes it work: market factors, economic cycles and company fundamentals all have to cooperate. It is not a set-and-forget trade.

The workbook's Fund CAS (Example 10.6), 1 April 2022 to 31 March 2023.

The fund buys Rs 1 crore of a 12% convertible bond (face value Rs 1,000, conversion ratio 25:1), financed with Rs 20 lakh of its own capital and Rs 80 lakh borrowed at 10%. It shorts 50,000 shares at Rs 40, paying a borrowing fee of Rs 5 a share. During the year the company pays a Rs 2 dividend, and the share ends at Rs 42.50.

Borrowing cost      Rs 80 lakh × 10%          = − Rs 8,00,000
Coupon              Rs 1 crore × 12%          = + Rs 12,00,000
Borrowing fee       50,000 × Rs 5             = − Rs 2,50,000
Dividend foregone   50,000 × Rs 2             = − Rs 1,00,000
Conversion          10,000 bonds × 25 = 2,50,000 shares
                    2,50,000 × Rs 42.50 − Rs 1 crore = + Rs 6,25,000
Short covered       50,000 × (42.50 − 40.00)  = − Rs 1,25,000
                                                ──────────────
Total                                           + Rs 5,50,000

Return on the fund's Rs 20 lakh = 5.50 ÷ 20 = 27.50%

Every figure reconciles. Now notice what drove it: the Rs 6.25 lakh conversion gain came from the share rising. The short covered only 50,000 of the 2,50,000 shares the bonds convert into — one-fifth — so most of the equity exposure was unhedged.

Chapter 10, section 10.1.3 (Convertible Arbitrage Strategy), defines the strategy and works Example 10.6. Chapter 10 carries 12% weight, the highest in the paper, and its worked strategies are prime calculation material. Expect a question on which legs are long and short, what the borrowing fee and foregone dividend are, and a return calculation from the example's cash flows.

• Long the convertible, short the equity — not the reverse.
• Dividends on shorted shares are a cost to the fund, not income.
• The borrowing fee is for borrowing shares to short; the 10% borrowing cost is on money borrowed to buy the bonds. Two different costs.
• Return is measured on the fund's own capital (Rs 20 lakh), not on the Rs 1 crore position.
• "Riskless" is the workbook's aspiration, not its example. The section calls the strategy riskless and independent of stock price movements, then says it can be riskier with changing macro conditions. In Example 10.6 the short covers one-fifth of the conversion shares and the profit depends on the share price rising. Treat it as a hedged strategy with real residual risk.
• Unverified claim: the workbook says that had the share price fallen, the fund would not convert and would close the short "with a net gain of 15%". No workings are shown for that figure; do not try to derive it.