How to choose among Vanguard's
Money Market and Money-market-like Funds?
Alternate Title: Is a bond fund's Yield worth its Duration?
Overview
Problem statement
(Readers who are just interested in the answer may jump straight to the Summary section at the bottom while glancing at the only table below.)
Data
- Vanguard Federal Money Market Fund (ticker: VMFXX)
- Vanguard Prime Money Market Fund (VMMXX)
- Vanguard Ultra-Short-Term Bond Fund Investor Shares (VUBFX)
- Vanguard Short-Term Treasury Index Fund Admiral Shares (VSBSX)
- Vanguard Short-Term Treasury Fund Investor Shares (VFISX)
- Vanguard Short-Term Federal Fund Investor Shares (VSGBX)
I will compare them in what I believe is the "right way". (By the way, this method of analysis applies to other types of bonds funds as well and not just these ones; see Footnotes section however.)
| Fund | Ticker | Average Duration |
SEC Yield |
Price Range |
Comments | Sherman Ratio |
|---|---|---|---|---|---|---|
1
|
VMFXX
|
76 days | 1.63% | constant |
7.8
|
|
2
|
VMMXX
|
91 days | 1.85% | constant |
7.4
|
|
3
|
VUBFX
|
1.0 year | 2.29% | 0.80% |
2.3
|
|
4
|
VSBSX
|
1.9 years | 2.42% | 1.96% |
1.3
|
|
5
|
VFISX
|
2.0 years | 2.10% | 2.50% | Dominated by 4 |
1.1
|
6
|
VSGBX
|
2.2 years | 2.32% | 2.39% | Dominated by 4 |
1.1
|
Table-related Notes
- All data except the last two columns was copied from Vanguard, as of May 15, 2018.
- For VMFXX & VMMXX (the first two entries), what is listed under "Average Duration" is actually "Weighted Average Life". Vanguard doesn't quote a duration for them.
- "SEC Yield" represents the current estimate of annualized yield, as of May 15, 2018.
- "Price Range" denotes the percentage difference in the 52-week high and low prices, as calculated by Vanguard (not me).
- "Sherman Ratio" was calculated by me by using the formula given by 100 x SEC yield / Average Duration expressed in years.
Definitions
- Yield is another name for interest income.
- Duration is an approximate measure of a bond's price sensitivity to changes in interest rates. If a bond has a duration of 6 years, for example, its price will rise about 6% if its yield drops by a percentage point (100 basis points), and its price will fall by about 6% if its yield rises by that amount. (Source: Google)
Analysis
Typically, one would like to maximize yield. (Yield represents interest income.) If this were the only concern, one would pick fund 4 (VSBSX) with an SEC yield of 2.42%.
However, more yield typically comes with more risk. To minimize risk, one ought to pick the fund with the least Average Duration. This will minimize the possibility of loss of principal due to rising interest rates. Note that I have presented the fund with the lowest duration first and in order of increasing duration. So, VMFXX has the lowest interest rate risk while VSGBX has the highest interest rate risk.
If minimizing duration was the only concern, one would pick fund 1 (VMFXX), but this comes at the expense of sacrificing yield. The SEC yield of VMFXX is 1.63% which is less than that of VSBSX that was selected two paragraphs above.
We immediately see that funds 5 and 6 are inferior to fund 4 because even though their Average Duration is greater than fund 4, their SEC yield is not higher. (This may be a short-term, transient anomaly in the data, as "SEC yield" can change daily. If it's not an anomaly, then my comment stands, which means that funds 5 and 6 ought to be avoided in favor of fund 4.)
The extent to which one can lose principal is captured in the 3rd column from the right which is labelled "Price Range", which means the following. If the future is going to be a repeat of the past 52 weeks, and if the fund in question is bought at its 52-week high price and sold at its 52-week low price, then the amount of loss would be what's displayed in this column. It's the most extreme loss, in all likelihood. We see that fund 5 (VFISX) has had the biggest price range and is therefore the worst fund in this aspect. But we shouldn't really care that much about fund 5 because it is dominated by fund 4. More importantly, we see that as we progress from fund 1 to fund 4, i.e. as duration increases, the Price Range also increases. This is to be expected and confirms the theory (which is something that's not being covered here).
We are now done with the analysis.
How to pick among funds 1-4? (We ignore funds 5 & 6 because they are dominated by fund 4, as explained above.)
The investor who cannot and doesn't wish to tolerate any additional risk ought to pick fund 1. This fund has the lowest Average Duration (safest), something which comes at the expense of having the lowest yield.
The investor who wishes to maximize yield and is willing and able to tolerate additional risk ought to pick fund 4. This fund has the higher SEC yield, which comes at the expense of having the highest duration (riskiest). How much risk would this investor really be taking? Here, the Price Range comes in handy and suggests that if the future were to be a repeat of the past, this investor would lose at most 1.96% in principal in conjunction to earning 2.42% in yield over one year. His net earnings would be 2.42% minus at most 1.96% which equals 0.46% or higher. In other words, the prospect of earning a 2.42% yield comes with the possibility of this yield shrinking to 0.46% over one year.
We can easily repeat the calculation in the above paragraph for fund 3 as well. However, we can also turn to the Sherman Ratio which captures the trade-off between yield and duration in a single number. The Sherman Ratio was created by DoubleLine Funds and Jeffrey Gundlach's team. It is the ratio of yield to duration. Qualitatively, it is the ratio of "benefit" to "risk", so the higher the better. We can think of this ratio as duration-adjusted yield. We can also think of this ratio as "slope" in a two-dimensional graph where yield is plotted on the y-axis and duration is plotted on the x-axis; it is the slope of the line connecting the origin to a specific fund's yield and duration.
The Sherman Ratios for funds 1-6 appear in the right-most column. The Sherman Ratios indicate that funds 1 and 2 (with Sherman Ratios in the 7-8 range) have substantially higher duration-adjusted yield than funds 3 and 4 (whose Sherman Ratios are in the 1-2.5 range).
Before having looked at the Sherman Ratios, I would have probably chosen fund 3, but now that I've seen the Sherman Ratios and noticed the large difference in the Sherman Ratios of funds 3 and 2, I would probably opt for fund 2.
When comparing two funds, one needs to assess for oneself whether the incremental yield increase (in going from the lower yielding fund to the higher yielding fund) is worth the incremental increase in duration. For example, in going from fund 1 to fund 2, the incremental yield increase is 13% (i.e. (1.85% - 1.63%) / 1.63% = 0.13 = 13%) while the incremental increase in duration is 20% (i.e. (91 - 76) / 76 = 0.20 = 20%). Personally, I would make this jump because the Sherman Ratios are very close (7.8 and 7.4).
Other factors not considered here but which may be worthy of consideration are as follows:
The bond funds which are the subject of this discourse have similar if not identical credit ratings.
We are now done with the analysis.
Decision Time
The investor who cannot and doesn't wish to tolerate any additional risk ought to pick fund 1. This fund has the lowest Average Duration (safest), something which comes at the expense of having the lowest yield.
The investor who wishes to maximize yield and is willing and able to tolerate additional risk ought to pick fund 4. This fund has the higher SEC yield, which comes at the expense of having the highest duration (riskiest). How much risk would this investor really be taking? Here, the Price Range comes in handy and suggests that if the future were to be a repeat of the past, this investor would lose at most 1.96% in principal in conjunction to earning 2.42% in yield over one year. His net earnings would be 2.42% minus at most 1.96% which equals 0.46% or higher. In other words, the prospect of earning a 2.42% yield comes with the possibility of this yield shrinking to 0.46% over one year.
We can easily repeat the calculation in the above paragraph for fund 3 as well. However, we can also turn to the Sherman Ratio which captures the trade-off between yield and duration in a single number. The Sherman Ratio was created by DoubleLine Funds and Jeffrey Gundlach's team. It is the ratio of yield to duration. Qualitatively, it is the ratio of "benefit" to "risk", so the higher the better. We can think of this ratio as duration-adjusted yield. We can also think of this ratio as "slope" in a two-dimensional graph where yield is plotted on the y-axis and duration is plotted on the x-axis; it is the slope of the line connecting the origin to a specific fund's yield and duration.
The Sherman Ratios for funds 1-6 appear in the right-most column. The Sherman Ratios indicate that funds 1 and 2 (with Sherman Ratios in the 7-8 range) have substantially higher duration-adjusted yield than funds 3 and 4 (whose Sherman Ratios are in the 1-2.5 range).
Before having looked at the Sherman Ratios, I would have probably chosen fund 3, but now that I've seen the Sherman Ratios and noticed the large difference in the Sherman Ratios of funds 3 and 2, I would probably opt for fund 2.
When comparing two funds, one needs to assess for oneself whether the incremental yield increase (in going from the lower yielding fund to the higher yielding fund) is worth the incremental increase in duration. For example, in going from fund 1 to fund 2, the incremental yield increase is 13% (i.e. (1.85% - 1.63%) / 1.63% = 0.13 = 13%) while the incremental increase in duration is 20% (i.e. (91 - 76) / 76 = 0.20 = 20%). Personally, I would make this jump because the Sherman Ratios are very close (7.8 and 7.4).
Other factors
- Expense Ratio
- Fund size, also known as "Assets Under Management" (AUM)
- Other factors
In general, expense ratio is to be minimized. Too small of a fund size might be a sign of a young or neglected fund.
For the above set of funds, I did look at these other factors but judged them as secondary.
Afterthoughts
Question: What happens in a rising interest rate environment? (We are currently living through a rising interest rate environment because the U.S. Federal Reserve has been raising interest rates.)
Answer: The yields on funds 1 and 2 are likely to increase with increasing interest rates. So are the yields on funds 3-6. However, funds 3-6 are likely to suffer a loss of principal too.
SEC Yield
The important question is whether this quantity is before or after fund expenses. Ideally, we ought to base our comparison on after-fee yield. I believe the SEC yield is an after-fee quantity based on my interpretation of this quote from Vanguard's website: "The SEC yield for a money market fund is calculated by annualizing its daily income distributions for the previous 7 days." The key word is "distribution" which has the meaning of a cash payment from the fund to the fund shareholder.
Average Duration
If you are comparing bond funds (or bonds) with differing credit ratings (e.g. Treasury vs. corporate vs. investment grade vs high yield), it would be a mistake to blindly maximize Sherman Ratio. The right thing to do would be to adjust the Sherman Ratios for differences in credit rating.Answer: The yields on funds 1 and 2 are likely to increase with increasing interest rates. So are the yields on funds 3-6. However, funds 3-6 are likely to suffer a loss of principal too.
Footnotes
Here are some fine points for more advanced readers.
The important question is whether this quantity is before or after fund expenses. Ideally, we ought to base our comparison on after-fee yield. I believe the SEC yield is an after-fee quantity based on my interpretation of this quote from Vanguard's website: "The SEC yield for a money market fund is calculated by annualizing its daily income distributions for the previous 7 days." The key word is "distribution" which has the meaning of a cash payment from the fund to the fund shareholder.
Average Duration
- For funds 1 and 2, there was no reported Average Duration and I had used their Weighted Average Life when calculating Sherman Ratios. This may be possibly incorrect theoretically, but I'm pretty much convinced that my thinking is correct from a practical point of view.
- I have used the terms "Average Duration" and "Duration" interchangeably. Let me clarify the difference. A single bond has a duration. The duration of a bond fund is a function of its bond holdings' durations and it is this quantity that's called Average Duration. The right way to calculate this Average Duration is to calculate a weighted average where the weights are proportional to the amount of capital invested in each bond. For a crude analysis, an equally-weighted average would probably do.
- If we wish to know a bond's duration very approximately, we can say that it is the same as the bond's maturity. I.e. a bond maturing in 10 years has a duration of 10 years, crudely speaking.
- The starting point for a quantitative understanding of Duration is (1) to write the expression for the price P of a hypothetical bond which has one cash flow F at future time T, and then (2) to differentiate it with respect to interest rate 'r' (i.e. calculate dP/dr), and then (3) to write an expression for dP/P by rearranging terms. The expression in step 1 is
- Duration in the way that I have explained it in the previous step is also known as "Modified Duration". It is described in Wikipedia here. There's also another kind of duration known as "Macaulay Duration" (also described in the same Wikipedia article). They are close cousins of one another and almost the same. So, for practical purposes it doesn't matter which one we use. (I like Modified Duration better because it has a well defined meaning which is dP/P. So, which definition is Vanguard using? Based on their comments when I searched their website for "duration", I think they are using Modified Duration.)
P = F / (1 + r)^T
The bond funds which are the subject of this discourse have similar if not identical credit ratings.
Summary
We worked our way through a procedure for selecting the most appropriate fund based on (a) yield and (b) duration. Yield is a measure of income while duration is a measure of risk. All else being equal, yield is to be maximized and duration is to be minimized.
The Sherman Ratio is the ratio of yield to duration and may also be called duration-adjusted yield. It may be used to rank bond funds, with the highest Sherman Ratio fund usually being the most desirable.
Which fund would I have chosen? Fund 2. It has the second highest Sherman Ratio. I was willing to forego the highest Sherman Ratio fund because I felt the additional yield was worth the additional duration risk.
Disclaimer: This analysis is not meant to be advice, only educational. By relying on it, you are implicitly agreeing to assume full responsibility for its consequences and hold me harmless from any and all liability. If you don't think you have understood it, please do not use it.
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