Part of this investigation involved looking at yield to maturity (YTM) and current yield for the bonds, and it occurred to me that it might be interesting and even educational to some Bogleheads to compare yield to maturity (YTM) and current yield for the individual bonds to SEC Yield and distribution yield for a bond mutual fund that might own these bonds. I'll start with the individual bonds, since I think they're easier to understand, and then draw the parallels to the yields for the bond fund.

At first I looked at AAA muni bonds only, since I probably wouldn't consider owning individual bonds with a lower credit rating. But then I saw that about 75% of the bonds in the Vanguard California Intermediate-Term bond fund (VCADX, Admiral Shares) were rated AA, so I decided to look at AA bonds instead, even though I probably wouldn't buy them. I searched the Fidelity website and found 12 AA-rated CA muni bonds that were close to a 5-year term to maturity. Here are the averages of the relevant numbers for the 12 bonds:

Term to maturity: 4.97 years.

Duration: 4.53 years

Coupon: 3.64%

Price: 109.83

YTM: 1.57%

YTW: 1.25%

Current yield: 3.3%

YTW = yield to worst, which factors in the call options on the bonds; e.g., one bond has a coupon rate of 5% and a YTM of 2.4%, but a call provision makes it likely that the bond will be called before maturity, lowering the YTW to 0.9%. So YTW probably is the more relevant number if I were going to buy the bond.

Note that the current yield of 3.3% is much higher than the YTM of 1.57% and the YTW of 1.25%. Using the average numbers from above, the current yield is calculated by dividing the average coupon payment by the average price (I'll assume annual coupon payments for simplicity):

3.64/109.83 = 3.3%

The YTM is much lower because the bonds will all mature at a price of 100 (assuming no defaults), which is 9.83 less than the current average price. The loss of that 9.83 over the 5-year holding period reduces the YTM to 1.57% (not even factoring in the call provisions).

Now let's compare these numbers to VCADX. Here are the relevant average numbers as of 9/30/2014:

Stated maturity: 9.6 years

Duration: 4.9 years

Coupon: 4.1%

Price: 11.76

SEC yield: 1.65%

Average YTM: 1.7%

Distribution yield: 3.00%

Note that although the average maturity is much higher at 9.6 years, the average duration is only a little higher at 4.9 years vs. 4.5 years for the individual bonds. Note that the average coupon and YTM for the fund are in the same ballpark as for the bonds, and the distribution yield for the fund is close to the current yield for the bonds. This is a key take-away.

Since the average coupon rates for the bonds and the fund are quite a bit higher than the yields to maturity, the bonds are priced above face value (par), and current yield (bonds) and distribution yield (fund) are quite a bit higher than YTMs. The latter was shown in the calculation earlier by dividing coupon payment by current price.

The way Vanguard calculates distribution yield results in a number that is very close to the current yield calculation for a bond. If we divide the most recent distribution amount on 9/30/2014 by the price on 9/30/2014, and annualize it we get:

0.02890 / 11.76 / 30 x 365 = 2.99%

The only difference between this calculation and the Vanguard calculation resulting in 3.00% is that VG uses the average price during the month instead of the price on the date of the distribution (reinvest date):

Another thing to note is that the average YTM for the fund was pretty close to the SEC yield on 9/30/2014. SEC yield is basically an average YTM over the previous 30 days. So both SEC yield (as mandated by the SEC) and distribution yield (as calculated by Vanguard), involve some averaging over the previous month.Vanguard wrote:Distribution Yield: The fund's current monthly income dividend per share, annualized (by dividing by the number of days in the month and multiplying by 365) and shown as a percentage of the fund's average NAV during the month.

If the bond fund were to hold all of it's bonds to maturity and buy no more bonds, and none of the bonds defaulted or were called, the share price would gradually decrease, just as the average price of the individual bonds will gradually decrease. So other than the unknown rate at which the coupon payments could be reinvested, the YTM would be a good indicator for the total return over the holding period for the collection of bonds or the bond fund.

Of course the fund does not just hold a collection of bonds to maturity, but is constantly buying and selling bonds, and maintaining an average maturity and duration at an intermediate-term target. And this bond fund is actively managed, as are many other Vanguard bond funds, so without looking at the individual holdings over time, it's hard to say exactly what the Vanguard bond fund managers are doing. I've seen some puzzling relationships between SEC yield and distribution yield over time for some Vanguard bond funds, and have posted about that elsewhere.

Oh, and back to the original point of the investigation. Even with a combined federal and state marginal income tax rate of 50%, which is much higher than my marginal rate, the after-tax yield of a direct 5-year CD earning 2.52% (best I know of currently) beats the tax-free yield to worst of 1.25% for the AA muni bonds, even without accounting for the credit risk and higher term risk of the bonds.

Kevin