Hedging Question

[danshirley]

Here's a hedging question that I have never been able to answer to my own satisfaction:
If I hold 100 shares of TLT how much TBT would I need to buy to completely hedge my risk??

[yclept]

This is a little dated:
seekingalpha.com/article/91860-how-about-this-for-a-hedge-combo-tbt-and-tlt
I'm going to compare a few months of later data. I'm going to use Yahoo's adjusted close numbers and assume that will account fully for dividends, though it will make for a bump in the road each month when TLT pays.

[yclept]

The answer should be 50 shares of TBT to hedge 100 shares of TLT. The question, of course is how well correlated is the leveraged TBT to the unleveraged TLT (which, I assume, is able to just invest in the bonds directly and thus doesn't have to use other derivatives to attain its stated goal).
As far as I can tell, the correlation is pretty good. I downloaded data from the last six months from Yahoo. The correlation for the two series of data shows as -.99, which is almost perfect. From 8/9/10 through 1/6/11, TLT gives a change in price (adjusted close) of 6.33%, while TBT has -7.72%, which again is pretty close. Using the adjusted close, of course, means that the dividends from TLT are rolled into the price, and even then it was a bit lower in absolute value.
I checked another period to examine a time when the VIX was high (it's been low the last six months). For that, I used the six month period from 9/2/09 through 3/2/10. In that case, the correlation coefficient shows as -0.96, which is still pretty good. TLT returned 5.79% while TBT was -7.32%.
The only reason I can think to want to exactly hedge these two against each other would be to sell well OTM covered calls against both of them expecting them to expire worthless. I don't know what one would have to do if one side or the other started to get close to the money. I guess one could just ride it out and let that side get called away. I don't know if ETF options trade American or European -- seems to me that if they trade American and got called away early it would leave one with a sort-of (but not really) naked position on the other side that isn't what the original strategy called for. It wouldn't be naked in the conventional sense, but the underlying position could lose quite a lot (by then unhedged) while waiting for the call to expire.
I'm not a statistician by any means. Maybe there's something amiss with the correlations I think I'm finding above. If one goes out aways the premiums look pretty attractive to me. For just one example, I'm seeing $0.84 bid on the June 48 call. That's almost $10 out of the money, and I would think pretty likely to expire worthless. I'm sure if I really understood the Greeks, I'd have a better based view than "pretty likely"! I'm working on them, but right now for me, they're a sword in the armory, not slung from my belt.
I'll try to post the spreadsheets later. Right now the dog is telling me it's past his dinner time.

[yclept]

high vic download

Attachments:

high vic download.csv.jpg (6.12 KB)

[yclept]

low vic download

I kept these in .csv since any spreadsheet should be able to view them.

Attachments:

low vic download.csv.jpg (5.3 KB)

[tyfighter3]

Dan, have you looked at using a 2x or 3x ETF. I would think that it would take less stock than a regular one would.

[danshirley]

"The answer should be 50 shares of TBT to hedge 100 shares of TLT"
Shares or dollars??

[yclept]

Good grief, what a mistake! I should have said dollars of course.

[danshirley]

Yclept:
You are getting a ratio of change of TLT to TBT of 6.33/7.72 = .79 .
Thus if I have 100 shares of TLT at a close on Friday of 92.35 and I want to hedge 100% with TBT on Monday at the open your figures say I need to buy $9235*.79 = $7295 of TBT which is 190 shares.
If TBT was 2X TLT we would have expected to need to buy .5(9235) = 4617 = 120 shares.
Is that how you read it??
As to why one would want to do this, in fact I have 100 shares of TLT which I am holding for dividends and for selling calls. I am just looking at the various possibilities for hedging the value of the TLT stock until things stabilize on the treasuries front.
You are right about the issue of using TLT or TBT in such a pair for covered calls. If one gets called you then get the other naked. It's easy enough of course to replace the called member of the pair or sell the uncalled member.
Here's a recent article on the TLT/TBT subject:
dragonflycap.com/2010/12/shorting-america-the-debt/

[danshirley]

Ty:
Isn't TBT a 2X ETF?? Do you have a suggestion of something else to hedge TLT??

[rovo]

I deleted the contents of this post of mine because it contained incorrect information. My bad and apologies for the misinformation.

[danshirley]

TLT:

The investment seeks results that correspond generally to the price and yield performance, before fees and expenses, of the Barclays Capital U.S. 20+ Year Treasury Bond index. The fund generally invests at least 90% of assets in the bonds of the underlying index and at least 95% of assets in U.S. government. It may also invest up to 10% of assets in U.S. government bonds not included in the underlying index. The fund also may invest up to 5% of assets in repurchase agreements collateralized by U.S. government obligations and in cash and cash equivalents.

TLT is the 20+ Year Treasurey Bond Index .... not 2x.

TBT:

The investment seeks daily investment results, before fees and expenses and interest income earned on cash and financial instruments, that correspond to twice (200%) the inverse (opposite) of the daily performance of the Barclays Capital 20+ Year U.S. Treasury Bond Index. The fund invests in derivatives that Proshare Advisors believes should have similar daily return characteristics as twice (200%) the inverse of the daily return of the Index. It invests typically the rest of the assets in money market instruments. The fund is non-diversified

[yclept]

It's becoming painfully clear to me that I do not understand the meaning of a correlation coefficient. I never took statistics and over the years have just fumbled around the periphery of it.
The results on the attached spreadsheet completely baffle me, but the one thing I think I can say with some degree of certainty is that trying to hedge two shares of TLT with one of TBT doesn't work -- correlation coefficients be damned!
Or to be a bit more specific, it hasn't ever worked over a 3 month period, a 6 month period, a 9 month period, or a 1 year period. Nor has it worked to start a portfolio with $1000 of each ticker and bring it forward for the full time that TBT has been in existence.
I guess I'm going to have to put this in the category of medieval mapmakers and just label it "Here lie monsters", because it's clearly terra incognita to me.

Attachments:

TBTTLT.ods.jpg (253.27 KB)

[clarkrl2]

I believe the easy way to find the value for any given day would be to take the close of TBT and multiply by 2 then divide this value into the close of tlt. Then for 100 shares you would multiply by 100.

[TLT/(TBT*2)]*100

For todays close [92.85/(37.94*2)]*100=122

While it's true that the 2:1 ratio is probably not the true correlation I believe unless you have a very large position the values will not differ by more than a share or two. Also each day the value of shares would change very slightly.

[danshirley]

I believe clark is correct.

Using the theoretical 1:2 ratio the formula for the number of shares would be :
(TLT/(TBT*2))*100 which today would be 122 shares.

Using Yclept's actual data it would be:
(TLT/(TBT*1.26))*100 which today is 194 shares.

This of course shows that historically TBT had been less than the theoretical 2X TLT over the longer term . This is because TBT is made up of futures and, like all of these multiple ETF's, is computed to be 2x the daily... and the ratio changes slightly every day.

It's funny how we bandy about TBT being 2x the Barclay's Capital 20+ Year U.S. Treasury Bond Index without a firm grasp on what that means.

I thank everyone for this exercise as it has firmed up how I would use TBT to hedge TLT should I decide to do so.

Right now I hold 50 shares of TBT as I was waiting to get the concept clarified... which this exercise has done. Today I Will fill out my TBT holding.

Hmm... should I go up to 192 or just take the theoretical 122 I'll have to decide. With 50 shares of TBT I am theoretically 50/122 = 40% hedged. If I go to 100 shares I'll be approximately 80% hedged.

chart.finance.yahoo.com/z?s=TLT&t=3m&q=c&l=off&z=l&p=s&a=v&p=s&lang=en-US®ion=US

Maybe TLT has bottomed out.

[rovo]

I prefer to just look at the delta change over a period of time.

Yesterday TBT declined by -1.04%
TLT increased by +0.54%
The ratio for yesterday was (1.04 / 0.54) = 1.93 or it took 1.93 shares of TLT to exactly counter balance 1 share of TBT.

[clarkrl2]

rovo your calculation should be $1.93 of TLT to $1 of TBT. Which for danshirely's 100 shares of TLT would require about 127 shares of TBT using Monday's close. The main point I'm making is that since your % change was change in dollars not shares the calculated ratio 1.93 to 1 would be dollars not shares.

[rovo]

clarkrl2, No argument from me on your previous post. A big "duh" from me. I'll just shut-up now.

[yclept]

upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Gunbarrel-Heavenly.jpg/800px-Gunbarrel-Heavenly.jpg

I still don't understand why one would want to hedge a position unless the intent is to sell otm covered calls against both sides. It feels to me like putting one ski on forwards and one backwards and heading down gunbarrel at Heavenly Valley. The first mogul is going to stop you cold.

[danshirley]

Yclept is really stumped by this strategy. I must admit that I made the post as something of an academic exercise to see if anyone could actually figure out how to use TBT as a hedge. I would give the class a 'B' on this one.
I have one more thing to say but I need to tell a story first:
Many years ago before my wife was my wife she was my lab technician. She was trying to get her master's in biostatistics and had passed everything but Math Stat. She had taken Math Stat twice and dropped it because she just couldn't wrap her brain around it.
I was on faculty by virtue of my position as lab director and could take any course for free. So I signed up for Math Stat along with her and with a joint effort we both managed to pass . She needed that degree to qualify for a Public Health scholarship which payed her Medical School tuition.
Now what has that got to do with anything:
Yclept: The Correlation Coeficient is way too gross a statistic to use the way you were trying to use it. 'R' is used to detect correlations in seemingly random data and not to use as a way to compare strength of correlation between two things that have obvious causal relationships.

Like many commonly-used statistics, the sample statistic r is not robust[10], so its value can be misleading if outliers are present. Specifically, the r is neither distributionally robust, nor outlier resistant. Inspection of the scatterplot between X and Y will typically reveal a situation where lack of robustness might be an issue, and in such cases it may be advisable to use a robust measure of association. Note however that while most robust estimators of association measure statistical dependence in some way, they are generally not interpretable on the same scale as the Pearson correlation coefficient.

Statistical inference for Pearson's correlation coefficient is sensitive to the data distribution. Exact tests, and asymptotic tests based on the Fisher transformation can be applied if the data are approximately normally distributed, but may be misleading otherwise. In some situations, the bootstrap can be applied to construct confidence intervals, and permutation tests can be applied to carry out hypothesis tests. These non-parametric approaches may give more meaningful results in some situations where bivariate normality does not hold. However the standard versions of these approaches rely on exchangeability of the data, meaning that there is no ordering or grouping of the data pairs being analyzed that might affect the behavior of the correlation estimate.

en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient

[yclept]

Yclept: The Correlation Coeficient is way too gross a statistic to use the way you were trying to use it. 'R' is used to detect correlations in seemingly random data and not to use as a way to compare strength of correlation between two things that have obvious causal relationships.

This part I'll take on faith (reinforced by the results I was seeing)!

As to the rest:

CASSIUS: Did Cicero say any thing?
CASCA: Ay, he spoke Greek.
CASSIUS: To what effect?
CASCA: Nay, an I tell you that, I'll ne'er look you i' the face again: but those that understood him smiled at one another and shook their heads; but, for mine own part, it was Greek to me. I could tell you more news too: Marullus and Flavius, for pulling scarfs off Caesar's images, are put to silence. Fare you well. There was more foolery yet, if I could remember it.
(William Shakespeare, The Tragedy of Julius Caesar (1599)

[danshirley]

I am just going to look prospectively at the relationship in changes in price in TLT and TBT to see how accurate a hedge TBT is. I'll track the price change in each plus the value of a $10,000 investment in TLT(108 shares purchased at close on 1/7/2011) and a $5000 investment in TBT(130 shares purchased at the same time). Theoretically if TBT is a good hedge the net investment should remain almost unchanged. I'll note when the monthly dividends are paid.

Week Ending............Weekly Price Change.......Weekly Value change
................................TLT...............TBT...............TLT..........TBT
1/14/2011..............-.51..............+.36.............-$55........+$47

So the first week it's not too bad. The $10,000 investment in TLT lost $55 while the $5000 investment in TBT gained $47. I'll see how it goes from here.

To answer Yclept's question as to why anyone would do that.. the answer is that it would give you a 'risk free' return of 2.6% in dividends from TLT (accounting for the extra investment in TBT) AND allow you to write covered calls on TLT which would return another 3% or so (again accounting for the extra investment in TBT) giving you a net return of about 6%....risk free. Try to get that anywhere else.

BTW: in my real account where I am doing this on a trial basis, my 100 shares of TLT is up $3.50, my 100 shares of TBT is up $41.50 and my short on the 95 call is up $27 (net values).
How is this possible??? I don't know...that's why I'm going to track it more closely.

Note on Methodology:
Purists would say I am forgetting something very important: Rebalancing.
After one week my net investment in TBT is higher while my net investment in TLT is lower. I should rebalance by either buying more TLT or selling some TBT to maintain a constant relationship between the two investments. The change is too small to worry about right now but I will watch it as we go forward. Theoretically I should rebalance daily as TBT is itself rebalanced on a daily basis. We'll see how it goes.

[yclept]

Dan,
I think my earlier retrospective (post 13) study examines much of what you are beginning to track -- it started with $1000 of each. I just noticed that I attached .ods format (Open Office) which most people probably cannot read, though nobody complained of such. Here is the .xls file on the chance that the earlier file was unreadable.

Attachments:

TBTTLT.xls.jpg (270 KB)

[Deleted]

This message has been deleted.

[danshirley]

Yclept:
Thanks for the spreadsheet... I'll have time to go over it this coming week.
I'm on the road right now, down south where the weather is a little bit warmer:
www.accuweather.com/us/sc/myrtle-beach/29578/forecast-details.asp
Compared to back up north:
www.accuweather.com/us/ny/new-york/10007/forecast-details.asp

BTW:
Just before I left I had a clock repair service come in and take the insides of my old grandfather clock out for cleaning and servicing. When they did I saw on the inside the little gold plaque that has ingraved on it the date we bought the clock. It was the week after my wife and I were married... almost 40 years ago. My wife told me that for days after we got the clock I used to hum this little song:
www.acousticmusic.com/staines/MYGRANDF.htm
I grow old, I grow old,
www.bartleby.com/198/1.html

[yclept]

Continuing off-topic, one can see it's bitter cold here today: weather.yahoo.com/united-states/california/san-leandro-12797369/

Smart move getting the clock repaired/cleaned. Assuming the premise of the song is correct, I guess you'll have to keep ticking right along with it.

[danshirley]

After today's close my combined position is:
TBT +94.50
TLT -77.00

So the TBT position continues to more than adequately compensate for losses in TLT.

In addition the short call is + 67.00


What'll happen if TLT goes in the opposite direction?

[danshirley]

As of Friday's close my combined net position is:
TLT: +12
TBT: +24.50
Short call: +44

All positive... and net about the same as above.

[danshirley]

So a week later TLT has moved in the opposite direction, and I have added to the position so that now I have 225 shares of TBT and 200 shares of TLT for a dollar ratio of 8778/17782 = .493. So that's keeping me very close to the 50% mark on TBT/TLT.
So far I am down $298 on TLT and up $265 on TBT. This combo allows me to collect dividends on TLT ($32 a month per 100 shares) and sell calls on TLT ($212 for 3 month calls). So that is yielding me 192 +212 = 404 in 3 months or 1616 yearly. The annualized yield is then 1616/(17782+8778) = 1616/26560 = 6.08%.
Risk free.
Not world shaking but it fits what I wanted to do. Especially since right now TLT by itself is yielding only 3.94%, without any such protection.
I suppose I could also sell calls on TBT but I haven't done that yet. I have to be careful in selling the calls so that I am not called very frequently. It won't be a disaster if I AM called but it will require resetting the whole thing.

[danshirley]

Another week later:
TLT: -260
TBT: +217.55
Short call: +105
Dividends: 64
TOT= 126.55 in 36 days or an annualized 4.8%

TBT/TLT = 8716/17834 = .489

So we are deviating a little bit this week... TBT is a little behind in tracking TLT