Bond Call Arbitrage, Borrowing Costs, and Implied Default Risk
Summary
The document explains an example involving a bond trading near its announced call price before redemption. An investor buys the bond and borrows most of the purchase cost; the bond’s coupon accrual exceeds the borrowing cost if it survives until the call date. The difference is a potential gain, not a guaranteed return, because the issuer may default before redemption.
The accepted answer describes inferring a short-period default probability by setting expected profit to zero across default and survival outcomes, given a recovery-rate assumption. It calculates an example probability using stated prices, rates, and a 40% recovery assumption. The response also cautions that the result depends on recovery and credit exposure, while percentage-return claims change with the investor’s equity and leverage. The example is simplified: it omits transaction costs and notes that the borrowing amount used in the original illustration does not fully fund the purchase.
Key ideas
- A bond bought before its announced call may earn coupon accrual net of borrowing costs if it survives.
- The apparent arbitrage gain remains exposed to issuer default before redemption.
- An assumed recovery rate and zero expected profit can be used to infer period default probability.
- Reported returns depend on how much capital the investor contributes and borrows.
- The illustration omits fees and identifies a mismatch between the borrowing amount and purchase cost.
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Full text
# Security Analysis By Benjamin Graham Example Doubt
# Security Analysis By Benjamin Graham Example Doubt
So I was reading (trying to read) Security Analysis by Graham and I came across this example ("Example 1" in the image attached below) Being the noob at finance and quant that I am, I was unable to understand it. I think I understood the calculation part - interest expense/dividend gains etc. and the net profit figure of 40% but didn't really understand how were they able to buy the shares at 11 on Jan 15 1935, and the statement about borrowing $10 per share. How did that work out? What did the brokers actually do?
## Answer by Attack68 (score 1, accepted)
https://quant.stackexchange.com/a/49599
After announcement, in December, of the intention to call the bond in April at 11 the market price fell to 11 and apparently remained at 11 throughout January.
The broker could have purchased the bond at 11 mid January (no fee or commission) and received back in April a value of 11.15 (i.e. principal plus 6% annual interest chargable for 3 months).
The going rate for unsecured borrowing was 2% so the broker could have borrowed 10 (although he really needed to borrow 11 to fully-fund the purchase) and in April would pay 0.05 (although really 0.055) as interest on this borrowing.
So the (real) net gain to the broker over 3 months would be 0.15 - 0.055 = 0.095.
If the bond issuer went bust before April the broker would be exposed to default losses on the bond, so this 0.095 really represents the credit exposure risk for 3 months.
Under arbitrage free pricing you would estimate that the probability of default in the period as:
$$ 0 = \underbrace{PD * (RR * 11150 - 11055)}_{\text{default loss}} + \underbrace{ (1-PD) * 95}_{\text{no default gain}} $$
Supposing Recovery Rate (RR) is 40% you have Probability of Default (PD) is $\frac{95}{6730}=1.4\%$ chance.
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I have two complaints about the examples. One is the use of the words sure return. As above credit risk is involved for 3 months so this is misleading since it is not at all guaranteed. Second the 40% annual return on a \$1000 principal is an arbitrary calculation. If instead the investor has \$1 and borrows \$10999 his 'sure return' is \$95 or 9500% return. If the investor has \$10000 and borrows \$1000 then his 'sure return' is \$145 or 14.5% return. So this seems to me to be an uninformative statistic.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.