Standard deviation measure of risk for a bond fund?

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Theseus
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Standard deviation measure of risk for a bond fund?

Post by Theseus » Tue Feb 06, 2018 4:47 pm

I understand that standard deviation is a risk indicator for equities. But I am having hard time thinking that standard deviation is also a risk indicator for bond funds. Generally, most bond funds (at least ones I am interested in such as VWIUX) keep the bonds until they mature. So if you are a buy and hold/never sell type investor how important is standard deviation of the bond fund? Wouldn't the quality of the underlying bonds be a better indicator of the risk?

alex_686
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Re: Standard deviation measure of risk for a bond fund?

Post by alex_686 » Tue Feb 06, 2018 4:53 pm

For all of its faults, one of the great things about standard deviation (SD) is that it can be applied to almost any asset and it will produce actionable information. So yes, SD is a good tool. I have seen arguments that semi-var, or downward volatility, is better than SD (up and down).

Bonds get priced every day, there is risk in holding bonds to maturity, and bond funds often have a high turnover.

Consider a scenario where inflation jumps for 2% to 4% and bond yields go from 3% to 6%. Even if held to maturity you are still going to be out money.

As for the quality of the bonds - what do you mean by that? I sorta of know what you mean but take a closer look. Are you referring to the bond ratings? Markets often reprice bonds before official ratings come out. Back in 2008 you could buy AAA bonds for 80 cents on the dollar. Everybody knew that they were junk and the prices reflected that. SD would capture that, bond ratings lag. Or look at today. The credit spread is very narrow. SD can communicate that the risk / reward ratio has shifted.

lack_ey
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Re: Standard deviation measure of risk for a bond fund?

Post by lack_ey » Tue Feb 06, 2018 5:21 pm

Standard deviation (of the return series) is a measure of past realized volatility. To the degree that past volatility is predictive of future volatility and that future volatility is related to how you define risk, this has meaning. If you accept that for stocks, you should do the same for bonds.

Bond returns are variable over time, whether you keep them to maturity or not. It's just that the average return over the exact period until maturity in the event of no default is known (and no options exercised, or specified call date, assuming a non-floating rate bond, not some kind of convertible or other structure). But that exact period is probably not of any interest to you, especially as an investor in a bond fund.

Bonds are more predictable than stocks for a number of reasons, especially relating to the structure of payments and the eventual maturity. Furthermore, the properties depend on the characteristics of the issuer, the term, and other considerations that are known and can be priced in. These make a larger difference than in stocks. A 30-year Treasury bond is a significantly different kind of thing than a 4-week Treasury bill. But how would you price and understand that difference without knowing anything about the past returns?

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Re: Standard deviation measure of risk for a bond fund?

Post by dbr » Tue Feb 06, 2018 6:28 pm

lack-ey's description is a good one. The point of emphasis is that SD of returns is part of the description of what the past and expected future behavior of the returns is. Risk, on the other hand, is a word that does not mean anything until a person specifies exactly what he means to talk about. Absent anything else specific that someone wants to talk about, people in financial discussions simply define risk as the SD of returns and it doesn't mean anything more or anything less than that. What relationship exists between the quality rating of bonds and the SD of returns could be inferred from the fact that lower rated bonds have higher returns and higher SD of returns than higher rated bonds. Bonds of longer duration have higher returns and higher SD of returns than bonds of shorter duration.

jalbert
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Re: Standard deviation measure of risk for a bond fund?

Post by jalbert » Tue Feb 06, 2018 7:18 pm

Sample variance or sample SD from historical samples is pervasive because it is easy to calculate. True risk is the variance of future return over some holding period of interest, but nobody knows how to determine that.
Risk is not a guarantor of return.

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Phineas J. Whoopee
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Re: Standard deviation measure of risk for a bond fund?

Post by Phineas J. Whoopee » Tue Feb 06, 2018 7:36 pm

Theseus wrote:
Tue Feb 06, 2018 4:47 pm
... Generally, most bond funds (at least ones I am interested in such as VWIUX) keep the bonds until they mature. ...
Most bond funds very much do not do that. It's a common misconception, but it's not your fault because a lot of outlets claim they do.

As for Vanguard's Intermediate-Term Tax-Exempt Fund Admiral Shares, VWIUX, the statutory prospectus makes no such commitment.
On page 19 of their Municipal Bond Funds Statutory Prospectus, Vanguard wrote: ...
The Fund has no limitations on the maturity of individual securities but is expected to maintain a dollar-weighted average maturity of 6 to 12 years
...
Do you have a specific source for your statement that Vanguard's Intermediate-Term Tax-Exempt, in particular, holds bonds to maturity?

PJW

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Re: Standard deviation measure of risk for a bond fund?

Post by abuss368 » Tue Feb 06, 2018 7:48 pm

Phineas J. Whoopee wrote:
Tue Feb 06, 2018 7:36 pm
Theseus wrote:
Tue Feb 06, 2018 4:47 pm
... Generally, most bond funds (at least ones I am interested in such as VWIUX) keep the bonds until they mature. ...
Most bond funds very much do not do that. It's a common misconception, but it's not your fault because a lot of outlets claim they do.

As for Vanguard's Intermediate-Term Tax-Exempt Fund Admiral Shares, VWIUX, the statutory prospectus makes no such commitment.
On page 19 of their Municipal Bond Funds Statutory Prospectus, Vanguard wrote: ...
The Fund has no limitations on the maturity of individual securities but is expected to maintain a dollar-weighted average maturity of 6 to 12 years
...
Do you have a specific source for your statement that Vanguard's Intermediate-Term Tax-Exempt, in particular, holds bonds to maturity?

PJW
Hi PJW -

Nice post! :beer
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grabiner
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Re: Standard deviation measure of risk for a bond fund?

Post by grabiner » Wed Feb 07, 2018 9:17 pm

The problem with using standard deviation as a risk measure is that you don't hold a bond fund in isolation; you hold it as part of your portfolio. A long-term Treasury bond fund has a high standard deviation because it loses value when interest rates rise. An intermediate-term junk bond fund has a high standard deviation because it loses value when junk bonds are likely to default. The Treasury fund is a better diversifier for a portfolio containing stock, as the junk-bond fund will decline when the stock market also declines. (And I don't like long-term Treasury funds either, but for a different reason; long-term bonds are attractive to insurance companies, so individual investors don't get compensated adequately for the risk.)
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stlutz
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Re: Standard deviation measure of risk for a bond fund?

Post by stlutz » Wed Feb 07, 2018 9:32 pm

Do you have a specific source for your statement that Vanguard's Intermediate-Term Tax-Exempt, in particular, holds bonds to maturity?
In the case of *this particular fund*, it seems that they actually do hold a lot of bonds to maturity. The average stated maturity of the bonds in the fund is 8.9 years. If they were holding to maturity I would expect that 1/ (8.9 * 2) = 5.6% of the funds holdings would be ready to mature in less than 1 year. According to the VG website, 4.3% of their bonds mature in 1 year. So not that far off.

This fund is unusual in this regard. Intermediate Term Treasury Index holds bonds until they have 3 years of maturity left. Total Bond index holds them until there is 1 year left.

All of that said, whether the fund holds to maturity has no real bearing on the riskiness of the fund. Standard deviation, duration, and credit quality are all good indicators to determine the actual riskiness. The fact that VWIUX is holding a lot of bonds to maturity is interesting, but in the end, not terribly relevant except possibly that it lowers the fund's trading costs.

Theseus
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Re: Standard deviation measure of risk for a bond fund?

Post by Theseus » Thu Feb 08, 2018 2:29 pm

OP here.

Thanks for the replies.

I am familiar (at least I think) with risk adjusted return for the equity mutual funds. Essentially if a fund is beating its benchmark, you have to adjust the fund's return by the amount of risk the fund took to generate those returns to derive risk adjusted return (of course adjust for expenses as well). SD here indicated how risky the fund is relative to it's benchmark.

I am still unclear is SD is a good risk measure for the bond funds. Let's say as part of my overall portfolio design, I need to allocate 10% of my total assets to the intermediate term municipal bonds in a taxable account. Primary purpose of this allocation is to manage a specific risk profile at the portfolio level and secondary purpose is the tax free income. I am considering following three options.

1. VWIUX - SD 3.02 ,ER 0.09
2. FLTMX - SD 2.76, ER 0.35
3. Custom bond portfolio - not sure how to determine SD here, ER around 0.40

So if SD is truly a risk indicator for bond funds also, I should be looking at FLTMX as it is 10% less SD. But its expense ratios is much higher. I am trying to determine if I am truly paying to reduce the risk. And does the risk adjusted return calculation for the bond funds same as for the stock funds?

Does this question make sense?

alex_686
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Re: Standard deviation measure of risk for a bond fund?

Post by alex_686 » Thu Feb 08, 2018 2:48 pm

Theseus wrote:
Thu Feb 08, 2018 2:29 pm
3. Custom bond portfolio - not sure how to determine SD here, ER around 0.40

So if SD is truly a risk indicator for bond funds also, I should be looking at FLTMX as it is 10% less SD. But its expense ratios is much higher. I am trying to determine if I am truly paying to reduce the risk. And does the risk adjusted return calculation for the bond funds same as for the stock funds?
Some quick points. Get the monthly total return of your custom bond portfolio for the past 2 or 3 years and plug the numbers in a spreadsheet. Bang, you got your SD. The simplicity of SD is one of its virtues.

I would focus on the expected return and SEC yield and not the expense ratio. Expense ratio is important only in the sense that it is a drag on the return you get so keep your eyes focused on what really matters.

I am not sure what risk adjusted tools you use for equities but many of them work just as well with bonds as with stocks. I am thinking specifically of the Sharpe Ratio. Heck, that even allows you to compare bonds verse stocks.

Lastly, use subjective wisdom as well as cold numbers. Honestly, the SD for your 2 asset classes is not that much different. The difference may well be within the error bars for when predicting future risk adjusted return. Let history guide you but don't treat it as a iron rule.

jalbert
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Re: Standard deviation measure of risk for a bond fund?

Post by jalbert » Thu Feb 08, 2018 2:49 pm

So if SD is truly a risk indicator for bond funds also, I should be looking at FLTMX as it is 10% less SD. But its expense ratios is much higher. I am trying to determine if I am truly paying to reduce the risk. And does the risk adjusted return calculation for the bond funds same as for the stock funds? 
A higher expense ratio decreases risk-adjusted return of whatever bond portfolio is being held because you are handing more of the bond yield over to the fund manager. This does not reduce risk to compensate for the reduced return.

To assess risk of a bond fund, the more important measures are duration, and the credit quality, liquidity, and types of bonds held. High standard deviation would be a red flag for a bond fund, but it is otherwise not that useful of a measure for managing risk of a bond fund.
Risk is not a guarantor of return.

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Epsilon Delta
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Re: Standard deviation measure of risk for a bond fund?

Post by Epsilon Delta » Thu Feb 08, 2018 3:20 pm

stlutz wrote:
Wed Feb 07, 2018 9:32 pm
[Vanguard's Intermediate-Term Tax-Exempt] fund is unusual in this regard. Intermediate Term Treasury Index holds bonds until they have 3 years of maturity left. Total Bond index holds them until there is 1 year left.
There are two distinct differences between the funds mentioned that help to explain this.

A tax exempt fund should be tax managed. Investors will be displeased if the managers convert tax exempt interest into taxable capital gains. This provides an incentive to hold to maturity.

The municipal market is much more fragmented (the index has 40822 issues) than the corporate market (9706 issues) or the treasury market (116 issues). This means the municipal market is much less of a commodity. The more idiosyncratic individual bonds are the harder they are to value and the more work is needed to make sure you trade them at a fair value. If you treat them as a commodity from time to time somebody with specific knowledge will pull a fast one on you. Not trading avoids this.

alex_686
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Re: Standard deviation measure of risk for a bond fund?

Post by alex_686 » Thu Feb 08, 2018 3:30 pm

jalbert wrote:
Thu Feb 08, 2018 2:49 pm
To assess risk of a bond fund, the more important measures are duration, and the credit quality, liquidity, and types of bonds held. High standard deviation would be a red flag for a bond fund, but it is otherwise not that useful of a measure for managing risk of a bond fund.
To counter, how do you quantify the risk associated with the different risks of duration, credit quality, etc. The risks in each of these dimensions are not stable nor are the relationships. One answer is SD.

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grabiner
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Re: Standard deviation measure of risk for a bond fund?

Post by grabiner » Thu Feb 08, 2018 7:57 pm

Epsilon Delta wrote:
Thu Feb 08, 2018 3:20 pm
stlutz wrote:
Wed Feb 07, 2018 9:32 pm
[Vanguard's Intermediate-Term Tax-Exempt] fund is unusual in this regard. Intermediate Term Treasury Index holds bonds until they have 3 years of maturity left. Total Bond index holds them until there is 1 year left.
There are two distinct differences between the funds mentioned that help to explain this.

A tax exempt fund should be tax managed. Investors will be displeased if the managers convert tax exempt interest into taxable capital gains. This provides an incentive to hold to maturity.
And that would normally happen if munis are sold a year before maturity, because yields decline as durations shorten. For example, suppose a fund buys a muni for $1000 with a 3% coupon. One year from maturity, the yield is likely to be 1%, and thus the bond will be worth $1020 (for a guaranteed $1030 the next year). If the fund sells the bond, it has a $20 capital gain. If it waits until maturity, the capital gain goes away and the $30 coupon offsets the $20 price decline.
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jalbert
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Re: Standard deviation measure of risk for a bond fund?

Post by jalbert » Thu Feb 08, 2018 8:23 pm

alex_686 wrote:
Thu Feb 08, 2018 3:30 pm
jalbert wrote:
Thu Feb 08, 2018 2:49 pm
To assess risk of a bond fund, the more important measures are duration, and the credit quality, liquidity, and types of bonds held. High standard deviation would be a red flag for a bond fund, but it is otherwise not that useful of a measure for managing risk of a bond fund.
To counter, how do you quantify the risk associated with the different risks of duration, credit quality, etc. The risks in each of these dimensions are not stable nor are the relationships. One answer is SD.
Because of our limited knowledge of the distribution of future returns, not every risk can be quantified accurately.
Sample SD is fairly sensitive to sample bias, and does not capture risks that don't materialize. Intermediate treasuries and intermediate corporate bonds have very similar sample variances in many time periods, but different risks.
Risk is not a guarantor of return.

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