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I am interested in comparing the value of bank Certificates of Deposit (CDs) with brokered CDs, to determine whether one is undervalued relative to the other. A brokered CD is basically a vanilla bond which can be bought at new issue and traded thereafter on an (albeit illiquid ) secondary market. A bank CD is a term deposit with no secondary market (you are not allowed to sell them to another investor), but the owner has the option to put it back to the issuer at par any time before maturity subject to an Early Withdrawal Penalty (EWP). The EWP is typically some prespecified fraction of the total interest which would have been earned had the CD been held to maturity. So a bank CD is basically a non-tradeable putable bond (American option) where the option premium is paid only if exercised (rather than included in the new issuance price like a conventional putable bond). Since both bank CDs and brokered CDs are FDIC insured, there is no credit risk differentiation between them, regardless of the issuer. I am considering only non-callable CDs.

Let's look at current 2y CDs as an example. The current cheapest 2y new issue brokered CD off Vanguard yields 1.70%. It's a bit harder to compare bank CDs because the EWPs vary, but the current cheapest 2y bank CD off RateBrain is 1.85% from Popular Direct with a 270 day EWP, which seems about average. So the put option premium is 1.39%, paid only if exercised. I’m not much up on options, but my first thought was that since the put option is initially sold at-the-money, the delta is 50% and if we equate that with the probability of expiring in-the-money then we could say that the present value of the premium payment is 50% * 1.39% = 0.69%. Now the bank CD yields 15bp more than the brokered CD and the duration is 1.95, so the present value of the extra yield is 0.29% which reduces the effective price of the option to 0.40% up-front. I priced on Bloomberg a 2y expiry ATM American put option on the on-the-run 2y maturity treasury bond (yielding 1.50%) and came up with a premium of 0.59%, so on that basis it looks like the bank CD underprices the put option by 0.19% and is the more valuable investment.

This surprises me because I assumed that the bank CD would overprice the put option, given that it is sold to investors who mostly have no ability value the option. However I do see three problems with the preceding approach:

1) Since the expiry of the put option equals the maturity of the bond, it will always expire at-the-money (ignoring the possibility of default and early redemption at par with FDIC insurance payout). Therefore unlike standard American equity options which I believe are never (except for special circumstances) optimal to exercise before maturity, it seems that this "expiry=maturity" bond put option should always be exercised before maturity because it will always expire worthless, but I have no idea when is the optimal time to exercise. Even so, since rates could go either way is the probability of exercise still 50%?

2) The CD put option can’t be sold so it should be worth less than the standard treasury bond put option. Even although the standard treasury bond put should be exercised some time prior to maturity, presumably before that time it is better to sell it rather than exercise it otherwise you lose the remaining time value. The CD put being non-tradeable forces you to sacrifice the time value, although the expected value lost seems to depend on the expected time of exercise which is investor-specific.

3) Suppose you can correctly value the CD put option and remove it from the equation, you are still left with having to value the non-tradeable vanilla bond component. Theoretically it seems you could “synthetically sell” a non-tradeable treasury-esque bond by selling treasury futures against it, which would lock in the mark-to-market value and ensure that you receive at maturity the price you would have received had you been able to sell it when you wanted. So a non-tradeable bond is like a tradeable bond with the obligation when you sell it to finance the purchaser until maturity at the implied treasury futures funding rate (approximately Libor?). But the price of this obligation seems to depend on a) the investor’s own funding rate; and b) the likelihood of the investor actually incurring the obligation by selling the bond. As to a), I'm not sure how one would go about estimating the funding rate of the average CD investor, or even whether there is such a thing. And b) is again investor-specific.

So, can anyone think of an objective way to value a bank CD relative to a brokered CD? Or is the best we can do to turn the problem on its head and assume that they are fairly valued and impute the observed price differential to be the cost of the tradeability option embedded in standard tradeable putable bonds?

The only remotely related thing I could find on the internet was this paper, but I couldn’t easily understand it and see how much bearing it had on the problem in hand.

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