Hi David,

Can you discuss Table 1.4 of Tuckman.I think that is mentioned in AIM but you seemed to have missed it completely.

Thanks
Sipani

Hi Sipani,

I’ll put that into an annotated spreadsheet, in case it’s helpful.

The “easy” step is: identify the arbitrage opportunity. That simply means: if a bond is mis-priced there is an arbitrage opportunity. So, here there is a cheap bond (market price < price implied by using discount factors).

* If cheap bond: buy the cheap bond, short its replicating portfolio, or
* If rich bond (market price > price implied by using discount factors), short the rich bond and buy its replicating portfolio

The “harder” step is creating the replicating portfolio, in the appendix, which is a sort of reverse bootstrapping. But, if all prices are fair, the cash flows to/from the replicating portfolio should equal cash flows to/from the bond. So 1.4 is an elaboration on that:

There are two sections
Top rows: the subsequent inflows/outflows. Cash outflows for the shorted replicating portfolio (i.e., it was shorted, so money collected today for outflow obligations over time - i like to think of this shorting as like being in the position of a corporate bond issuer: get the proceeds today for future stream of obligations). For the purchased “cheap” bond, the reverse: an immediate cash outflow in exchange for a series of cash inflows (+5.375) for the coupons and principal that will be due. So, these two future streams are identical by design; by definition the four bonds replicate the future cash flows (5.375 = 5.375 and 105.375 = 105.375). So, that’s the key to the whole thing, two investments (1. cheap bond, 2. replicating portfolio) that produce an identically offsetting stream of future cash flows.

Bottom line(row): the initial up-front transaction. the price for the cheap bond is slightly less than what is received for shorting the replicating portfolio (111.041 < 110.938). That’s the arbitrage. It happens on day 0 and the profit is immediate (riskless)

David