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I was curious about the following threads on NAV and went to Vanguards website for their fund prospectus. It is generally an informative piece - worth the read on general issues with investing in bonds.

However my specific question was how much are Vanguard managers allowed to uses derivatives to manage their interest rate exposure and basically their effective or modified duration. This is their blanket statement regarding all their fixed income funds:

Futures, options, and other derivatives may represent up to 20% of a Fund's total assets. Generally speaking, a derivative is a financial contract whose value is based on the value of a traditional security (such as a stock or bond), an asset (such as a commodity like gold), or a market index (such as the Standard & Poor's 500 Index). Investments in derivatives may subject a Fund to risks different from, and possibly greater than, those of the underlying securities, assets, or market indexes. The Funds' derivatives investments may include bond futures contracts, options, straddles, credit swaps, interest rate swaps, total rate of return swaps, and other types of derivatives. Losses (or gains) involving futures can sometimes be substantial—in part because a relatively small price movement in a futures contract may result in an immediate and substantial loss (or gain) for a fund. Similar risks exist for other types of derivatives. For this reason, the Funds will not use derivatives for speculation or for the purpose of leveraging (magnifying) investment returns. The reasons for which a Fund may invest in futures and other derivatives include:

■To keep cash on hand to meet shareholder redemptions or other needs while simulating full investment in fixed income securities.

■To reduce the Fund's transaction costs or to add value when these instruments are favorably priced.

None of that bothers me as deriatives used sensible can lower transaction costs - etc etc. But to see 20% makes me wonder how generally comparing interest rates and bond NAV's is going to be difficult when the fund manager has so many options (pun intended) to manage the account outside of buying and selling in the cash market.

Anyway just some thoughts


The PDF was called fixedinc.pdf and the quote came from page 35 of the prospectus.
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"But to see 20% makes me wonder how generally comparing interest rates and bond NAV's is going to be difficult when the fund manager has so many options (pun intended) to manage the account outside of buying and selling in the cash market."


Interesting idea, since I really have no satisfactory explanation for the data I've posted. I don't know how to find historical data on the funds, but I suspect the 20% is unusual, if ever, and I'm guessing the prospectus you looked at is not for the bond index funds, just the bond picking funds (Iseem to remembers separate reports for the two categories).

Here's the current short term holdings for the funds I've looked at on the shrinking NAV issue:

1% for Total Index, 1.8% for Long Corporate, 8% for Intermediate Treasury.

I would agree that the use of derivatives and short term instruments would make a simple comparison between a tracking yield (e.g., 10-year Treasuries) and a fund's NAV problematic. But the shrinking NAV data correspond to the actual SEC yields on the funds—Treasury yields are easy to find historically, so the provide a useful starting point. The use of derivatives should, somehow, show up in the SEC yields.

My concern remains that even if you manage to buy and reinvest at the average NAV each interest rate cycle, when you go to sell your shares in the long hereafter, you will be selling for an average loss, so your total return will be less than the compounded average yield over your time of investing. Compounded average yield is what you get from laddering individual bonds (or CDs).
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Here's another shrinking NAV data point. I tried the Intermediate Index Fund, because the Total Bond Fund is probably more variable with maturities. I'm also going to assume, like with a Treasury ladder, that you don't reinvest dividends, just take the dividends and spend them or save them elsewhere.

If you bought shares on the fund on 12/29/95 you would have paid $10.37. If you cashed out on 12/29/05 you would have gotten back $10.37. However, the fund yield went from 5.87% to 4.88%.

Now, there may have been some capital gains distributions, but with the index funds in particular these seem to be small. Looking at the income returns (which include compounding through reinvested dividends), the initial yield would be about the average dividend for 10 years. So with durations of around 6, I think this fund is leaking around .5% per year over 10 years compared to buying a 10 year bond at the end of '95 with a 5.87% yield.
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For Nerds' Eyes Only:

Some interesting new angles on the shrinking NAV issue:

First, it looks like the realized capital gain on the Intermediate Index Fund is much more substantial than on the Total Bond Index Fund—a point worth pursuing for its own sake, in the ongoing attempt to understand how the Total Index works (I think more complicated than the Total Stock Market Index). Anyway, looking at the annual capital returns listed by Vanguard and comparing with change in NAV, over 10 years the annualized realized capital gain on the Intermediate Index was .367%, as was the total capital gain, while an estimate for total capital gain based on change in yield and an educated guess for duration would be around .6% annualized. With the Total Index, the realized gain was only about .176% annually, with the total capital return being .097%, again with an estimate for predicted capital return of about .6%. So, the realized capital gain (per Dan's suggestion) is much more important in accounting for leakage with the Intermediate Fund.

Now, if we break down the numbers over 5 and 10 year periods, things look very different.

Consider Total Index Fund: Over 10 years for 1996-2005, the total capital return was .97%, with 1.76% realized gain and loss of .79% to NAV ($10.14-$10.06), with yield dropping from 6.11% to 4.75%. From 2001-2006, the total capital return was 1.4%, with NAV rising from $9.96-$10.06, about 1%, so only about .4% of capital gain was realized. Yield dropped from 6.67% to 4.75%, so with 4.5 duration, we'd predict a total gain of about 8.6% (way less than 1.4%). From 1996-2000, the total capital return was -.43%, with a +.36 realized return and a loss of NAV of -.79% (I can't quite get the numbers to add up). The yield went from 6.11% to 6.67%, so with 4.5% duration, the predicted loss would be about 2.5%, over 2% more than the actual loss of .43%.

At any rate, even though the 10 year period and the most recent 5 year period show capital return leakage, for the first 5 years, there is actually some capital return improvement.

Something similar happened with the Intermediate Fund: Over 10 years, total capital return was 3.67%, all of it realized gain. Predicted gain was about 6% with yield drop from 5.87% to 4.88%. For 2001-2005, total capital return was 5.25% with 3.5% gain in NAV from $10.02 to $10.37 and 1.75% from realized capital gain (.35% annual). The yield went from 6.45% to 4.88%, with a duration of 6 predicting a gain of 9.42%, more than 4% below the actual 5.25% return. However, from 1996-2000, the total capital return was -1.58%, The NAV lost 3.375%, so the realized gain was 1.8% (.36% annualized). The yield went from 5.87% to 6.45% predicting a loss of 3.48% (with duration 6), almost 2% worse than actual loss.

Again, during the 1996-2000 period, when interest rates went up, the capital returns on both funds were about .4% better annually than predicted. During the 2001-2005 period, when interest rates fell, the Total fund fell short by about 1.4% annually, while the Intermediate Fund fell short by about 1% annually.

What any of this means, I do not have a clue.
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I checked the bond index prospectus and the language was similar but they removed the 20% cutoff presumably to a much lower and non-material number.

Second looking at some of the funds there is the call risk which gives the funds some negative convexity. This is especially more of an issue when corporate debt and CMO's show up in the index funds.

Also the funds might have be given a single weighted duration but the actual durations of the bonds along the term structure will be affected by twists in the yield curve differently (key rate duration are needed). Also with the call option effect of certain bonds and mortgage backed securities there should be differences between funds. My point is that duration is a linear approximation good for only 50bp of yield change on a parallel shift of the curve.

Anyway these are the sorts of things I want to look at (as well as the aforementioned use of derivatives) at least more my own education on bond portfolio management but I am having a hard time following the discussion as posted. Is there a way to post your data points in a table format? That would help me gain a better understanding of where to poke and prod :)) Not that in the end I will have added value but I will give it a try.

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Too hard to tabulate. I agree durations are variable and a bit of a crap shoot, but I think we can approximate well enough to see large discrepancies, although small ones could easily be explained away from the approximation.

However, I think your suggestion of call risk may be the key. We've talked about it before, but not tried to work through its impact on particular funds. It looks to me like the refinancing of mortgages could well explain much of the downward NAV drift, along with realized capital gains, which are stronger with other funds than the Total Index.

I went back to the Intermediate Treasury Fund. To make it easier, I won't give all the numbers, just summary:

From '96-'00 Capital return of ,54%, realized gain .82%, NAV loss .28%, yield down .11%, which with a duration of 5 comes out almost perfect.

From '01-'05 Capital Return of 5.03%, realized gain 4.2%, NAV gain .83%, yield down 1.14%, at duration 5 expected 5.7%, but probably within margin for error.

On the other hand, the GNMA fund, where refinancing risk is known to be an issue:

From '96-'00 Capital return of -1.42%, realized gain .43%, NAV loss -1.85%, yield down .33%. Duration on this fund is even more of a crap shoot, but with the yield down, there should be a gain not a loss, unless something else, like refinancing, is going on.

From '01-'05 Capital return of .89%, realized gain of .31%, NAV gain of .58%, yield down 1.81%. Choose any duration you like, I think 4-5 is reasonable, and the capital return is at least 5% below what is predicted from duration and change in yield. Since we know refinancing is an issue, and that the theoretical premium on mortgage securities at a given moment on which NAV is based goes to par with refinancing, this makes good sense as an explanation for the failure of the fund to capitalize on falling interest rates.

Since bond index funds have substantial holdings in mortgage securities, as well as some callable corporates, call/refinancing risk during falling interest rates looks like it covers a lot of the missing money (along with realized capital gains).

There may be some other things going one, but I think the falling NAV phenomenon is mostly explainable by realized capital gain plus refinancing/calls.

What the implications are for choosing bonds funds is worth extensive discussion. My initial thinking is bond index funds and GNMA funds are going to underperform during falling interest rates and I'd be looking toward long term corporate (with limited calls, which Vanguard does) or long term Treasury or TIPS fund, but only when interest rates are very high, because otherwise these funds will get hit hard with rising interest rates. GNMA will probably give a stable overall return if you get in above average interest rates, but won't benefit from falling rates like the others. Personally, I'm going to stop looking at the Cref Bond fund and start trying to figure out when and how I can transfer the money to an IRA where I can ladder on my own. I'm pretty sure that's a few years off, if then (I'm not interested in taking money out and paying taxes and Rothing). Something to ask the tax gurus about.
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For the callable bonds, the negative convexity will manifest itself on the lower end of the interest rate axis. As rather than price continue to increase (at an increasing rate) with a decrease in rates the bonds value will slow in approach the limiting "call" value. Going the other way - up in rates, this results in a price yield curve that will actually slow the NAV loss on interest rate increases. So the loss in NAV would have to occur either before the interest rates start their rise, or if while interest rates are rising, the bonds are called and the manager did not get enough of a discount to compensate for the call option.

Another item I have not seen in the mix is the reinvestment piece.

An example:

If you purchased a ten year treasury with a yield to maturity of 4% and then interest rates shoot up to 6% Whether you lose money, make money or break even depends on how long you hold the bond.

In the short run you lose money. Obviously with an increase in rates, the note would be worth less. About 14% less. So if you sold - you lose.

If you hold the note then you get to reinvest the dividends at the new (6%) higher rate. Over time this additional interest on interest will add up and if you hold to maturity you will have more money than if interest rates had remained at 4%.

So to put this in a bond fund perspective. If we buy when rates are low and then rates slowly increase, NAV goes down so, if our dividend remains the same we can now buy more shares at the lower NAV. In the end would

# Shares(i) X NAV(i) = # Shares(j) X NAV (j)

i = interest rate remains unchanged
j = interest rate increases

So when we return to "equilibrium" we are compensated for a lower NAV by having more shares?

Hey, what do you expect at ten to midnight?

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