**no risk of change in nominal price at maturity due to change in interest rates**, and a cheap put option--i.e., an early withdrawal penalty (EWP) of 60 days of interest (all yields and attributes as of today). However, a common concern is: what if Ally Bank changes the EWP or won’t let me do an early withdrawal? Fair question.

To evaluate this risk, I compare the total return of the CD to that of the bond fund under a variety of interest rate scenarios over the next 5 years; i.e., assuming I am unable to do an early withdrawal from the CD. A fairer comparison, assuming no early withdrawal, would be the PenFed 5-year CD currently yielding 2.25% (with a 1 year of interest EWP), but let’s assume I value the cheaper put option on the Ally CD enough to sacrifice the 50 basis points in yield (assuming no problem with early withdrawal, the Ally CD provides a higher return if you break it up until about 4 years).

I believe it’s reasonable to use the Vanguard Intermediate-Term Treasury Fund for a fair comparison. Like the FDIC-insured CD, it has no credit risk. The SEC yield is 0.89% (

**EDIT: for Admiral Shares**), average maturity is 5.2 years, and average duration is 5.2 years. You might prefer to compare the CD to something like Total Bond Market Index fund, but that fund has credit risk, so it’s not a fair comparison; but even so, the CD reward/risk still is asymmetrical compared to the bond fund, and I’d be happy to share those numbers once any flaws in my analysis are uncovered and corrected.

I understand that there are other considerations that might cause one to favor the bond fund (e.g., convenience, simplicity, liquidity, etc.), but here I just want to consider the financial returns of CD vs. bond fund, in isolation (i.e., not how it contributes to overall portfolio return; consider a portfolio of 100% fixed income if it helps). Thus, the primary consideration is the term risk of the bond fund.

Scenario 1: Interest rates are flat for 5 years. CD beats bond fund by 4.3% ($10K grows to $10,901 vs. $10,453).

Scenario 2: Interest rates increase 1% per year for 5 years. CD beats bond fund by 19.5% ($10K grows to $10,901 vs. $9,122)

Scenario 3: Interest rates are flat for 2 years, then increase 1% per year for 3 years: CD beats bond fund by 16.7% ($10K grows to $10,901 vs. $9,344).

Scenario 4: Interest rates drop to 0% in year 1, then remain at 0% for 4 years: CD beats bond fund by 3.8% ($10K grows to $10,901 vs. $10,507). Note that this is the best-case scenario for the bond fund that I can find, and the CD still wins.

I’m using a simple model, with these simplifying assumptions.

- Bond fund interest rates change linearly, so annual interest portion of return is the average of the rate at beginning of year and end of year.
- Annual change
**percentage change**in bond fund NAV = -1 x Duration x total annual interest rate change (EDIT:**in percentage points**).**EDIT**: Convexity not accounted for; i.e., current duration used for all calculations. - Total annual return for bond fund is sum of 1 and 2.
- Total return is compounded annually

**EDIT: This currently is my main interest; i.e., how big are the errors in using this simple model. Certainly the non-linear nature of the bond price/yield relationship (convexity) introduces some error, but how much? Enough to worry about? Even if we include convexity in the model somehow, are there other aspects of a bond mutual fund that introduce additional significant errors relative to a standard bond price/yield curve?**

So it looks to me like the CD can win by a lot or win by a little, but it always wins. If you add some credit risk to the bond fund for a higher yield, then the bond fund can win by a little, but can lose by a lot (in relative terms).

So what flaws do you see in this analysis?

Kevin

EDITs 2/23/2012:

- Changed a few things above based on what I've learned so far, and to make the statements more accurate or precise.
- I still think the CD provides superior risk/return compared to the bond fund, but probably not as much as indicated by the model. Still looking for ways to improve the model.
- Technical note: The duration used here is Modified Duration, not Macaulay Duration. I assume it's the former and not the latter that is published for bond funds, since it's the former that is used to estimate sensitivity of bond or bond fund price to yield change.