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?page1



1 Answer 1


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.


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.


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