Market timing 2-year treasuries using Martingale-style bets

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Rob Bertram
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Market timing 2-year treasuries using Martingale-style bets

Post by Rob Bertram »

[Split into a new topic from: Should I use margin to buy a balanced fund? --admin LadyGeek]
I have been looking at the 2-year treasury futures data and noticed something. If the price ever drops, I can buy more contracts, place a sell limit order at the average price. When the order executes, I effectively reset my basis to the lower price. And it looks like I can sell a couple ticks higher and cover my transaction costs.

As others have pointed out, this is a version of a Martingale betting strategy (wiki link). If the strategy has reasonable promise after rigorous discussion with forum members, I plan on using this strategy on the 2-year treasury portion of my leveraged portfolio experiment.
Last edited by Rob Bertram on Tue Oct 27, 2015 9:42 pm, edited 1 time in total.
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Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

One interesting feature of 2013 is that the 2-year note went from a low of 0.2% to 0.52% and finally settled at 0.38%, so there wasn't much yield to help with recovery.

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I am working on other periods as well, like 2004-2006. I haven't checked to see if there's data for 1994, but that is on my todo list.
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Re: Should I use margin to buy a balanced fund?

Post by lack_ey »

Have you thought more, changed your mind, or developed any further thoughts about what to do if the yield curve inverts or gets close enough to flat that the "carry" is negative?
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Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

My current plan is to close any position where the carry is negative. 2006 - 2007 would be an example of that. My strategy might change if the same characteristics of 2013 hold -- that I can always reset my basis to the lowest price. Someone else would effectively be paying the carry price for me.

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lee1026
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

I have been looking at the 2-year treasury data and noticed something. If the price ever drops, I can buy more and sell at the average price and effectively reset my basis. And it looks like I can sell a couple quarter ticks higher and cover my transaction costs. And about 80% of the time, it happens within 2 weeks.
What does "reset your basis" mean? It can't be a tax thing, because taxes don't work that way on futures.
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Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

It's a term that I made up. It means that my effective purchase price of that futures position is reset to the new (lower) price. For example, say that I have 5 2-year note contracts purchased at $110.00. The price drops to $109.50. I buy 10 more contracts at $109.5 and then set a limit order to sell 10 at the price of (110 + 109.5)/2 = 109.75. When the limit order executes, I will effectively have a position of 5 contracts that were purchased at $109.5.
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Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

I was a little surprised to see the following success rates for 2006:
1-day: 91.9%
3-day: 96.1%
2-weeks: 97.1%
4-weeks: 97.4%
6-weeks: 98.4%
8-weeks: 98.7%
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

It's a term that I made up. It means that my effective purchase price of that futures position is reset to the new (lower) price. For example, say that I have 5 2-year note contracts purchased at $110.00. The price drops to $109.50. I buy 10 more contracts at $109.5 and then set a limit order to sell 10 at the price of (110 + 109.5)/2 = 109.75. When the limit order executes, I will effectively have a position of 5 contracts that were purchased at $109.5.
If you are confident about your ability to buy at 109.5 and sell at 109.75, why not just do this all day long and forget about everything else in this discussion?
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

That is a good question. In short, I am looking at daily lows and highs, so I can at best complete the offsetting transactions over two days. I might have to wait a few weeks for the limit order to execute, so it's not necessarily something that can scale to several times a day.

In a similar thought, I was looking at how frequently I can execute a similar set of transactions except sell at one or two ticks higher than the average price to offset the transaction costs. That had a slightly lower success rate but is worth investigating. For example, sell N-1 contracts at the average price and 1 contract at average price +tick.
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

2 ticks is $30. Margin on a 2 year bond is $650 per contract. If you go to 50% margin, you will make a 2.5% return each time you pull this off. If you can do this every week on average, that is over 100% per year.

Forget about everything else!
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Re: Should I use margin to buy a balanced fund?

Post by ogd »

Rob: what you're talking about now is very short-term technical analysis, which many (or most) of us consider little better than numerology. Yes, you can beat a strategy out of the data, then watch it fail spectacularly. Happens over and over. This thread started on a much more sound basis.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

lee1026 wrote:2 ticks is $30. Margin on a 2 year bond is $650 per contract. If you go to 50% margin, you will make a 2.5% return each time you pull this off. If you can do this every week on average, that is over 100% per year.

Forget about everything else!
I hear what you're saying, but there are a few challenges with something that aggressive. For starters, I will need to tripple down on my current position, so I can be at most 33% leveraged. Next, I am not guaranteed that there will be a drop, so the the futures price will steadily increase and approach the spot price. I can look and see how frequently the price drops X ticks, but that is getting closer to what Ogd is saying about technical analysis.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

ogd wrote:Rob: what you're talking about now is very short-term technical analysis, which many (or most) of us consider little better than numerology. Yes, you can beat a strategy out of the data, then watch it fail spectacularly. Happens over and over. This thread started on a much more sound basis.
Yes! My reason for posting here is to have an open discussion about my ideas. Maybe I can step back and describe the fundamental thought of this analysis. I believe that there are core aspects of bonds driving the behavior that I am describing. Here is what I believe is accurate:
  1. Treasury futures are fairly priced to accurately represent the underlying treasury notes. For example, there is no credit risk. Term risk is the primary one. So we have: futures contract price = spot price - (pro-rata) dividend yield + cost of financing
  2. When yields increase, treasury futures have a similar point of indifference if held (and rolled) to duration.
  3. Increasing our bond position when yields increase reduces the recovery time as we are buying at the cheaper rate with higher yields.
I believe that these are characteristics exclusive to bonds, specifically treasuries (which have zero credit risk). Price and yield mathematically have an inverse relationship. If prices drop, then there is a mathematical certainty that the yield has increased.

I had earlier noted that 2-year treasury futures often have positive returns shortly after a yield increase. My original investigation was to see how "quick" that recovery time is. Looking only at contract price, that recovery time is often around 2-8 weeks. In other words, I lose 2 months of dividends in order to net back to zero. And I wasn't looking for a full recovery to a point of indifference, I was looking to see how quickly I could net to zero.

The next thought that I had was, can I "tax loss harvest" these and net to zero? I say that in quotes because what I really want to do is lower the price I paid for my position. So that is where I am now. If any of my reasoning is flawed, I would appreciate any feedback on how to correct it.

Right now, the idea is to buy 2N more contracts at the new lower price and sell N contracts at the average price. My position at the end will be the original N contracts, but I will be at 3N contracts for some amount of time. There is always the chance that the price will drop more before it recovers, so that increased risk has not yet been discussed.
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Re: Should I use margin to buy a balanced fund?

Post by selftalk »

What a great way to raise your risk tolerance. The answer is NO !
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Re: Should I use margin to buy a balanced fund?

Post by LiveSimple »

No Need.

Just live below your means, save and invest.

For most, money that comes easy, will go away easy !
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Rob Bertram
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

Rob Bertram wrote:It's a term that I made up. It means that my effective purchase price of that futures position is reset to the new (lower) price. For example, say that I have 5 2-year note contracts purchased at $110.00. The price drops to $109.50. I buy 10 more contracts at $109.5 and then set a limit order to sell 10 at the price of (110 + 109.5)/2 = 109.75. When the limit order executes, I will effectively have a position of 5 contracts that were purchased at $109.5.
Rob Bertram wrote:In a similar thought, I was looking at how frequently I can execute a similar set of transactions except sell at one or two ticks higher than the average price to offset the transaction costs. That had a slightly lower success rate but is worth investigating. For example, sell N-1 contracts at the average price and 1 contract at average price +tick.
Another idea would be to buy 2N +1 contracts at the low price and then sell N+1 at the average price. That would net a few ticks profit which would offset the transaction costs. Treasury futures cost $1.51 per trade, and this strategy is trading 3N contracts (2N buy + 1N sell). Each tick is worth $2000/128 = $15.625. So maybe something like buy 2N + RoundUp(0.3 * N/#ticks) contracts.

I haven't looked at the risk side of this yet. It will help answer the question, "Why not go 3N or 4N on a dip?"
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Re: Should I use margin to buy a balanced fund?

Post by market timer »

Rob Bertram wrote:Right now, the idea is to buy 2N more contracts at the new lower price and sell N contracts at the average price. My position at the end will be the original N contracts, but I will be at 3N contracts for some amount of time. There is always the chance that the price will drop more before it recovers, so that increased risk has not yet been discussed.
Sounds like a variation on a martingale betting strategy. In your analysis, consider not just the probability of winning, but the magnitude of loss as well.
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Re: Should I use margin to buy a balanced fund?

Post by backpacker »

Rob Bertram wrote:[*]Increasing our bond position when yields increase reduces the recovery time as we are buying at the cheaper rate with higher yields.[/list]
I've enjoyed this thread Rob. Thanks for sharing your experience!

This looks to me like you're basically applying a martingale strategy to short-term treasuries. [Ha! Looks like market timer beat me to this point by two minutes.] When you start losing, bet more money until you start winning. The original futures contracts won't recover any faster because you're adding money to your position.

Maybe this makes sense with treasuries because you are, in effect, guaranteed to eventually start winning, unlike other games of luck. I don't know. But I would be nervous if my leverage strategy depended on any of this.

I would think the reason to have both leveraged short treasuries and long treasuries would be to spread out your risk across the yield curve. That much makes sense to me.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

I definitely agree that it is a Martingale betting strategy on short-term treasuries. And unlike other risky scenarios like flipping a coin, I believe that the relationship between bond price and yield put the odds significantly in my favor. I'm hoping that some of our resident bond experts will help describe that advantage or identify my mistakes. So with bonds (and bond futures), my argument is not "if" the bet wins but "when".

Just to repeat some of my analysis, in 2006 (when rates went from 4% to 5%, and FFR > 2-year rate), this bet paid off 91.9% of the time on the first day and 96.1% within 3 days. So I need to understand what happened on the 21 days where the bet did not win. In 2013 (when rates when from 0.2 to 0.5), the bet paid off 72.5% of the time by the first day and 82.1% within 3 days.

Oddly, I believe that this reduces the long-term risk of the total portfolio. Though, I need to rebuild my risk model to incorporate the Martingale betting and run the model over the losing periods.
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Re: Should I use margin to buy a balanced fund?

Post by Park »

Rob, the original goal was to look into levering a stock/bond portfolio. My interpretation was that you accepted levering a stock portfolio, but wondered whether levering stocks and bonds together might be better.

As ogd has mentioned upstream, you're now changing your focus to short term technical analysis. In my experience, technical analysis is a synonym for market timing.

The purpose of your thread was to get feedback from others. I don't know many successful market timers, and of those that exist, not many will be posting to this thread.

I know that overconfidence has been my greatest failing as an investor.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

I will agree that there is analysis involved. Does that mean that the behavior I'm witnessing is invalid?

As a comparison, there is a lot of technical analysis around rebalancing in terms of how often vs bands. That does not invalidate MPT and the premise that risk diversification between uncorrelated assets increases risk-adjusted returns.
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Re: Should I use margin to buy a balanced fund?

Post by Kevin M »

Rob Bertram wrote: As a comparison, there is a lot of technical analysis around rebalancing in terms of how often vs bands. That does not invalidate MPT and the premise that risk diversification between uncorrelated assets increases risk-adjusted returns.
Perhaps, but the more I've thought about it, the more I've concluded that a lot of the analysis supposedly based on MPT and CAPM is flawed. The problem is that standard deviation of monthly or annual returns is used as the risk measure, but to evaluate risk-adjusted return for holding periods much longer than one month or one year.

MPT and CAPM are a single holding period models, so to apply these models to say a 20-year or 30-year holding period, we should be using standard deviation of 20-year or 30-year returns, as well as expected values for those returns, and we don't have nearly enough data to draw valid statistical conclusions for those periods. Not to mention that we don't know if historical returns are a good statistical representation of future returns.

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Re: Should I use margin to buy a balanced fund?

Post by lack_ey »

Who's even the market on the short side of short-term Treasury futures, other than speculators hoping for rate increases? Traders hedging a tiny bit of term risk out of short-term distressed credit plays? Some more complicated derivatives swaps/hedging scheme? Institutional arbitragers collecting the spread in the imputed borrowing costs for those on the long side?
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

Who's even the market on the short side of short-term Treasury futures, other than speculators hoping for rate increases? Traders hedging a tiny bit of term risk out of short-term distressed credit plays? Some more complicated derivatives swaps/hedging scheme? Institutional arbitragers collecting the spread in the imputed borrowing costs for those on the long side?
Speculators are net short:
http://www.reuters.com/article/2015/10/ ... L320151023

Lots of people want to bet that the Fed will raise rates, by the looks of it.
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Re: Should I use margin to buy a balanced fund?

Post by backpacker »

Kevin M wrote:
Rob Bertram wrote: As a comparison, there is a lot of technical analysis around rebalancing in terms of how often vs bands. That does not invalidate MPT and the premise that risk diversification between uncorrelated assets increases risk-adjusted returns.
Perhaps, but the more I've thought about it, the more I've concluded that a lot of the analysis supposedly based on MPT and CAPM is flawed. The problem is that standard deviation of monthly or annual returns is used as the risk measure, but to evaluate risk-adjusted return for holding periods much longer than one month or one year.

MPT and CAPM are a single holding period models, so to apply these models to say a 20-year or 30-year holding period, we should be using standard deviation of 20-year or 30-year returns, as well as expected values for those returns, and we don't have nearly enough data to draw valid statistical conclusions for those periods. Not to mention that we don't know if historical returns are a good statistical representation of future returns.
+137

The longer I invest, the more annoyed I get with the assumption that short-term distributions adequately predict long-term risk.
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Re: Should I use margin to buy a balanced fund?

Post by Day9 »

EDIT: Comment removed by user and moved to original thread
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

Implied finance costs for stock futures and bond futures are very different, mostly because on the stock side, you are asking the lender to take on the risk that the dividends will be cut. On the bond side, the dividend is effectively T-Bills. Implied financing for bond futures is roughly LIBOR. 0.25% ish.
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Re: Should I use margin to buy a balanced fund?

Post by ogd »

Rob Bertram wrote:I will agree that there is analysis involved. Does that mean that the behavior I'm witnessing is invalid?

As a comparison, there is a lot of technical analysis around rebalancing in terms of how often vs bands. That does not invalidate MPT and the premise that risk diversification between uncorrelated assets increases risk-adjusted returns.
No, the technical analysis around bands is about as worthless as all other technical analysis. It just doesn't matter. For example, if your starting premise had been "I plan to profit from the difference between monthly rebalancing and VBINX's continuous rebalancing", you'd have gotten the same rolling of eyes that you're seeing now.

The rebalancing bonus derives its power from elsewhere -- the typical and sound diversification argument that the market can't possibly price the other stuff in your portfolio, therefore for some combination of assets the pricing of a particular asset becomes favorable to the holder of that combination. Diversification provides a free risk reduction that you can transform into return with leverage.

By contrast, your thesis with Treasury timing is more like "the pricing of this widely known and widely watched asset is wrong in the short term, and I, Rob Bertram, will be the one to profit from this by looking at some graphs".
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

ogd wrote:
Rob Bertram wrote:I will agree that there is analysis involved. Does that mean that the behavior I'm witnessing is invalid?

As a comparison, there is a lot of technical analysis around rebalancing in terms of how often vs bands. That does not invalidate MPT and the premise that risk diversification between uncorrelated assets increases risk-adjusted returns.
No, the technical analysis around bands is about as worthless as all other technical analysis. It just doesn't matter. For example, if your starting premise had been "I plan to profit from the difference between monthly rebalancing and VBINX's continuous rebalancing", you'd have gotten the same rolling of eyes that you're seeing now.

The rebalancing bonus derives its power from elsewhere -- the typical and sound diversification argument that the market can't possibly price the other stuff in your portfolio, therefore for some combination of assets the pricing of a particular asset becomes favorable to the holder of that combination. Diversification provides a free risk reduction that you can transform into return with leverage.

By contrast, your thesis with Treasury timing is more like "the pricing of this widely known and widely watched asset is wrong in the short term, and I, Rob Bertram, will be the one to profit from this by looking at some graphs".
Just to be clear, my first premise is that pricing is correct.

We can forget about futures for a moment and focus on regular bonds/bond fund fundamentals. When yields increase and bond prices go down, we point at reinvesting dividends and say we are buying bonds with the new (higher) yield. If we hold and continue to reinvest dividends long enough , we will hit a point of indifference where the the total return from the new bonds at the higher yield would match the total return of the old bonds at the lower yield. This isn't technical analysis; it's math.

Instead of going all the way to the point of indifference, I only want to get to the point where my total return is greater than or equal to zero. It is significantly less than the full duration. For 2-year treasuries, we are talking weeks. Again, this isn't technical analysis, it's math.

The strategy that I am suggesting has me buy 200% more bonds (in addition to reinvesting dividends). I am now getting 3x the new yield. The amount of time it takes to get a total return of zero is now measured in days. This is still math. Why are people rolling their eyes?

Now I need to deal with the reality that yields change every day. This is where the technical analysis comes in. I need to understand what happens when yields increase for a year or for three years.
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Re: Should I use margin to buy a balanced fund?

Post by lee1026 »

We can forget about futures for a moment and focus on regular bonds/bond fund fundamentals. When yields increase and bond prices go down, we point at reinvesting dividends and say we are buying bonds with the new (higher) yield. If we hold and continue to reinvest dividends long enough , we will hit a point of indifference where the the total return from the new bonds at the higher yield would match the total return of the old bonds at the lower yield. This isn't technical analysis; it's math.
The math don't really apply to treasury futures. This is only the case as long as your borrowing costs remain constant, which have been true for the last few years, but may not remain true in the future. And since that risk is the risk that you are actually getting paid for, discounting that seems unwise.
Instead of going all the way to the point of indifference, I only want to get to the point where my total return is greater than or equal to zero. It is significantly less than the full duration. For 2-year treasuries, we are talking weeks. Again, this isn't technical analysis, it's math.
Again, I am not sure if I agree that is the correct math. The spread on the 2 year over LIBOR is around 30 bps. If the interest rates move against you by 50 bps, you will lose around 90 bps upfront. If LIBOR don't change, your spread will go to 80 bps. Still will take you about a year to fully recover. And again, that is assuming the Fed don't raise rates.
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

I agree that we need to go from a simple scenario of a single yield increase change to futures pricing. But we need to go in baby steps.

Can we agree for now that what I am describing is in fact bond math? And specifically treasures as they are assumed to not have credit risk. If we agree on this, then the next thing to look at is how the market prices a rate increase. Is it all at once, or is is more gradual over the year or years? Maybe a little of both?

The market doesn't always follow the FFR, but here is a good piece of information on FFR rate changes: http://www.newyorkfed.org/markets/stati ... drate.html

Here is data from Fred:
https://research.stlouisfed.org/fred2/graph/?g=2jP4
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Re: Should I use margin to buy a balanced fund?

Post by in_reality »

Rob Bertram wrote: Can we agree for now that what I am describing is in fact bond math? And specifically treasures as they are assumed to not have credit risk.
That is an assumption that probably holds but doesn't definitely always hold.

No political discussion is intended here, so please don't anyway make any.

However, if the dept. ceiling is not raised and the treasury has no money to pay bondholders, are you saying that you will still be safe?

I do not mean to make a doomsday prediction, as surely such a thing would only be temporary -- wouldn't it, but what would happen in the bond market if it did.

If you are going to honestly evaluate your idea, the notion of treasuries not having credit risk must be reexamined. That the treasury will not run out of money is not an assumption you can make. Where are you at if it's out of business for 30 days? What about the time to hold another election (less likely though)?

(again this is not political discussion, this is financial discussion on a case where the treasury does not have money to pay bondholders -- it's a possibility isn't it)
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

When it comes to the treasury defaulting, I'll fall back to what Larry Swedroe says: "it is as close to impossible as you can get and thus IMO should be treated as if it was. If that happens there are far worse problems anyway."
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Re: Should I use margin to buy a balanced fund?

Post by Day9 »

Rob Bertram wrote:When it comes to the treasury defaulting, I'll fall back to what Larry Swedroe says: "it is as close to impossible as you can get and thus IMO should be treated as if it was. If that happens there are far worse problems anyway."
While that is true, the price could still fluctuate because of changes in perceived default risk.

"The 2011 S&P downgrade was the first time the government was given a rating below AAA. S&P had announced a negative outlook on the AAA rating in April 2011. The downgrade to AA+ occurred four days after the 112th United States Congress voted to raise the debt ceiling of the federal government by means of the Budget Control Act of 2011 on August 2, 2011" Wikipedia
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Re: Should I use margin to buy a balanced fund?

Post by ogd »

Rob Bertram wrote:Instead of going all the way to the point of indifference, I only want to get to the point where my total return is greater than or equal to zero. It is significantly less than the full duration. For 2-year treasuries, we are talking weeks. Again, this isn't technical analysis, it's math.

The strategy that I am suggesting has me buy 200% more bonds (in addition to reinvesting dividends). I am now getting 3x the new yield. The amount of time it takes to get a total return of zero is now measured in days. This is still math. Why are people rolling their eyes?
I don't quite agree with the notion that the zero point is the target; as lee1026 says, you have borrowing costs so that's likely insufficient and might even move the zero out of reach for a long time. But granting that for a moment: the time to get to zero is proportional to the magnitude of a change vs starting yield. It's only small if the delta is small. If it's large (which btw is your better case, see below), then it can take a considerable time to recover. For a 0.5% increase from the current 0.66%, we're talking almost a year. With a 3x boost, it's still 3.5 months. Not days.

Meanwhile, you are far more exposed to future rate increases, and that's what the rolling of eyes is about. There are scenarios in which the yield increase does nothing to diminish the future risk, most significantly an inflationary jolt. You increase your holding because the Martingale-like strategy says you need it to recover in such and such timeframe, not because you can better afford to. The bond math is the easy and relatively unimportant part of this strategy; the lines you're spending your time studying are the bread and butter.

Here's a very unsound aspect of your strategy, if I understand it correctly: given two smaller increases, you'll have 9x your initial holding. With only one larger increase, you'll have 3x of your initial holding. Compare this to a rebalancing strategy, which is not path-dependent. A bad sequence of increases can lead you to a very bad place, I believe. For many a Martingale gambler, the path to ruin began with the apparently simple question of "what are the odds of 10 reds in a row".

I would be most afraid of the inflationary scenario I mentioned; it's something you don't see in 2003-2007 but would give you a pretty good beating, and the "potential energy" for such a slide is definitely there in the form of low rates and low predicted inflation (i.e. not priced in). To be exposed to this for the purpose of grabbing the small differences between 2 year yields and borrowing rate does not seem worth it to me.

P.S.: I know it's your thread, but you might consider starting a new one. The pages and pages of good discussion on balanced allocation efficiency have sort of taken an identity of their own :)
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Re: Should I use margin to buy a balanced fund? [Martingale treasury]

Post by LadyGeek »

Upon request by the OP, I have split this discussion into a stand-alone thread from Re: Should I use margin to buy a balanced fund?

Rob Bertram - Feel free to change the thread title. Just edit the Subject: line in Post #1.
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Rob Bertram
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Re: Should I use margin to buy a balanced fund? [Martingale treasury]

Post by Rob Bertram »

Thanks, LadyGeek! You are an inspiration and a scholar. I will definitely update the thread title and edit the OP for better background.
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Re: Should I use margin to buy a balanced fund? [Martingale treasury]

Post by Rob Bertram »

Okay, the conversation is going great, and we have a lot of points to cover. If we can dissect the strategy into smaller, more manageable points, I believe that we can discuss with greater clarity.
ogd wrote:I don't quite agree with the notion that the zero point is the target; as lee1026 says, you have borrowing costs so that's likely insufficient and might even move the zero out of reach for a long time.
Borrowing cost is important and deserves discussion, but can we table this point until we get to a better understanding of the core "Martingale betting" aspect of the strategy? It might be 5-10 more posts, but I definitely will return to it.
ogd wrote:the time to get to zero is proportional to the magnitude of a change vs starting yield. It's only small if the delta is small. If it's large (which btw is your better case, see below), then it can take a considerable time to recover. For a 0.5% increase from the current 0.66%, we're talking almost a year. With a 3x boost, it's still 3.5 months. Not days.
This I believe is the core of the strategy, so I want to make sure that everyone reading and discussing are phrasing things in the same context. For starters, let's focus on a single day's change. And as Ogd points out, we are talking about relative change in yield which is essentially a ratio of percent (or a percent of a percent which definitely makes my head hurt).

How can we establish reasonable bounds on what we frame as a daily change in the 2-year treasury yield? I will make an attempt, and please correct me if I go in the wrong direction. FRED has data on 2-year constant maturity treasuries going back to June 1st, 1976. I can calculate the daily change by comparing the current day's yield to the prior. I am only interested when rates increase, so I will ignore days when the yield goes down for now. Here are the results:
  • Average yield increase: 1.8643%
  • Standard deviation: 2.7190%
  • A 3-sigma change would be 1.8643% + 3*2.7190% = 10.0214% (Is it fair to round this down to 10%?)
If I frame this in today's current yields, a 3-sigma change from the current yield of 0.66% would be 0.66% * 0.10 = 0.066%. In other words, the yield would increase from 0.66% today to 0.726% tomorrow. Is 3 sigma enough? Five sigma is 15.4594%. That will take a current yield of 0.66% to 0.76%.

I am going to attempt to calculate the amount of time for the strategy to return to zero for the average, 3-sigma, and 5-sigma cases. I will start with a 0.66% yield and assume 2-year duration. Here goes:
  • Average case: The yield increases from 0.66% to 0.672%. The NAV of my bond position drops by 0.012% * 2 = 0.024%. I increase my position to 3x, so my effective yield is 3* 0.672% = 2.016%. It will take 365 * 0.024%/2.016% = 4.3 days to recover the loss from dividends. ***Note that 0.024% is well within the daily volatility of a 2-year treasury ETF.
  • Three-sigma case: The yield increases from 0.66% to 0.726%. The NAV of my bond position drops by 0.066% * 2 = 0.132%. I increase my position to 3x, so my effective yield is 3* 0.726% = 2.178%. It will take 365 * 0.132%/2.178% = 22 days to recover the loss from dividends. ***Note that 0.132% is within the daily volatility of a 2-year treasury ETF x3.
  • Five-sigma case: The yield increases from 0.66% to 0.76%. The NAV of my bond position drops by 0.10% * 2 = 0.20%. I increase my position to 3x, so my effective yield is 3* 0.76% = 2.28%. It will take 365 * 0.2%/2.28% = 32 days to recover the loss from dividends. ***Note that 0.20% is still within the daily volatility of a 2-year treasury ETF x3.
***If we use VGSH as an ETF proxy of a 2-year treasury, the average daily spread between high and low is $0.07 (Yahoo! Finance) with a share price of $61.20 or $0.07/61.2 = 0.11% of NAV. But wait! I just increased my position to 3x, so that is really 0.33% of my original. I am happy to take my gain as capital gains instead of dividend. I don't need the ETF to settle at the target price, I only need my limit order to execute.
ogd wrote:Meanwhile, you are far more exposed to future rate increases, and that's what the rolling of eyes is about. There are scenarios in which the yield increase does nothing to diminish the future risk, most significantly an inflationary jolt. You increase your holding because the Martingale-like strategy says you need it to recover in such and such timeframe, not because you can better afford to. The bond math is the easy and relatively unimportant part of this strategy; the lines you're spending your time studying are the bread and butter.
How can we quantify an inflationary jolt? Maybe I can look at data from the early 80s? FRED data only goes back to 1976, so I can't see '73-74.
ogd wrote:Here's a very unsound aspect of your strategy, if I understand it correctly: given two smaller increases, you'll have 9x your initial holding. With only one larger increase, you'll have 3x of your initial holding. Compare this to a rebalancing strategy, which is not path-dependent. A bad sequence of increases can lead you to a very bad place, I believe. For many a Martingale gambler, the path to ruin began with the apparently simple question of "what are the odds of 10 reds in a row".
There is definitely the exponential risk of multiple concurrent bets to consider. So maybe I can set a rule for maximum concurrency of 4 bets.
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Re: Should I use margin to buy a balanced fund? [Martingale treasury]

Post by market timer »

There seems to be the implicit assumption in several of these posts that the 2-year yield will eventually yield more than short term financing costs for an arbitrarily long period of time--long enough to recoup an initial capital loss from rates going higher. This is a false assumption. It may seem unlikely given the experience of the past 3 decades, but I would not base a strategy around a permanently upward sloping yield curve.
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Re: Should I use margin to buy a balanced fund? [Martingale treasury]

Post by Rob Bertram »

market timer wrote:There seems to be the implicit assumption in several of these posts that the 2-year yield will eventually yield more than short term financing costs for an arbitrarily long period of time--long enough to recoup an initial capital loss from rates going higher. This is a false assumption. It may seem unlikely given the experience of the past 3 decades, but I would not base a strategy around a permanently upward sloping yield curve.
You mean like 2006? At times, financing costs are 0.83% higher than 2-year yields.
Image

Here is what I discovered when I looked at 2-year treasury futures data for 2006.
Rob Bertram wrote:I was a little surprised to see the following success rates for 2006:
1-day: 91.9%
3-day: 96.1%
2-weeks: 97.1%
4-weeks: 97.4%
6-weeks: 98.4%
8-weeks: 98.7%
Edit: Changed the graph from FFR to LIBOR.
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Re: Market timing 2-year treasuries using Martingale-style bets

Post by lee1026 »

Five-sigma case: The yield increases from 0.66% to 0.76%. The NAV of my bond position drops by 0.10% * 2 = 0.20%. I increase my position to 3x, so my effective yield is 3* 0.76% = 2.28%. It will take 365 * 0.2%/2.28% = 32 days to recover the loss from dividends. ***Note that 0.20% is still within the daily volatility of a 2-year treasury ETF x3.
If you think 5 sigma event is only going to cost you 20 bps, I don't think this is the trade for you; you should be trading options. The option market is pricing a standard deviation at around around 6 bps. so a 5 sigma event is around a fall of 30 bps.

I won't worry about an increase in the borrowing rate for now, and in any event, when you buy a future, you lock in a financing rate until the future expires. But we should at a minimum include the borrowing rate that exist right now; 3 month LIBOR is at 0.32%. At a spread of 0.44% and a drop of 0.3%, you are looking at close to a year of recovery.
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Re: Market timing 2-year treasuries using Martingale-style bets

Post by Rob Bertram »

Well, remember that the context is a day. We can have consecutive 3-sigma days and go well above 30 bps change in total.

The aspect that I find fascinating is that it seems that I can recover a single day's drop in value by the next day with an amazingly high success rate. (Maybe someone will open my eyes and point out a huge flaw.) If so, that would make a string of 2- and 3-sigma days much more tolerable than a 5-sigma day.
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Re: Should I use margin to buy a balanced fund?

Post by HomerJ »

Rob Bertram wrote:I was a little surprised to see the following success rates for 2006:
1-day: 91.9%
3-day: 96.1%
2-weeks: 97.1%
4-weeks: 97.4%
6-weeks: 98.4%
8-weeks: 98.7%
How much do you lose if (when) the 8-weeks 1.3% chance comes up?
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Re: Market timing 2-year treasuries using Martingale-style bets

Post by HomerJ »

Rob Bertram wrote:The aspect that I find fascinating is that it seems that I can recover a single day's drop in value by the next day with an amazingly high success rate. (Maybe someone will open my eyes and point out a huge flaw.)
Um... it's not 100%? That's the flaw...

This is called picking up nickels in front of a steam-roller.

Easy money, until you slip one day and the consequences are huge.
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Re: Market timing 2-year treasuries using Martingale-style bets

Post by ogd »

lee1026 wrote:I won't worry about an increase in the borrowing rate for now, and in any event, when you buy a future, you lock in a financing rate until the future expires.
This is true for his original holding, but the Martingale'd additions are after the rate increase. They might not have higher profit at all.
Rob Bertram wrote:How can we quantify an inflationary jolt? Maybe I can look at data from the early 80s? FRED data only goes back to 1976, so I can't see '73-74.
That should still be instructive, yes. The primary fear is that your yield increases but it doesn't really mean anything good -- no better profits atop your borrowing rate, no reduced risk of future increases. This is without even mentioning that the money you're getting is worth less, which is probably a small effect over the time periods involved.
Rob Bertram wrote: 1.Treasury futures are fairly priced to accurately represent the underlying treasury notes. For example, there is no credit risk. Term risk is the primary one. So we have: futures contract price = spot price - (pro-rata) dividend yield + cost of financing
2. When yields increase, treasury futures have a similar point of indifference if held (and rolled) to duration.
Rob: is it a big leap of faith, then, to say that #2 too is priced in #1? I mean, everybody knows that bonds recover, it's not some new discovery or (more to the point of the last thread) something unique to your portfolio that the market can't possibly price in, like the exact level of equities.

So knowing that bonds recover, the market chooses to pay you X% more than the zero rate. This should tell you something about the risk involved. Then you lose Y% of that as borrowing costs. This seems like a losing proposition to me.

As for the data mining, I'll mostly bow out of that because -- like in technical analysis for stocks -- no amount of extrapolating the past is going to convince me that a strategy has such and such a priori probability of success. I haven't studied the exact number of crashes in bonds, but I know what happens in stocks -- all you need to do is tweak some knobs to avoid 2-3 big crashes and your strategy looks golden. Until the fourth, that is.

Something to consider is factoring into your "probabilities" (there should be a better name for that, with past tense more prominent) the yield curve configuration and weighting the scenarios that look like right now more. Because the yield curve means [priced-in] risk, not just profit.
Rob Bertram wrote:***If we use VGSH as an ETF proxy of a 2-year treasury, the average daily spread between high and low is $0.07 (Yahoo! Finance) with a share price of $61.20 or $0.07/61.2 = 0.11% of NAV. But wait! I just increased my position to 3x, so that is really 0.33% of my original. I am happy to take my gain as capital gains instead of dividend. I don't need the ETF to settle at the target price, I only need my limit order to execute.
One more generic remark -- you can't really count on limit orders to do anything positive for you -- can't use them to recover daily losses, can't use them to lower persistent spreads. You only use them to avoid negatives, like buying at a particular bad market configuration. The devil is in the details of "I only need my order to execute" -- when it doesn't it takes away your reward from the other scenarios, in spades. You should generally book exactly zero positive effects from limit orders.
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Re: Market timing 2-year treasuries using Martingale-style bets

Post by market timer »

Are you assuming that if the 2-year futures trade at some level intraday that you are guaranteed the ability to trade at that level? This is potentially problematic. To be safe, I think you should assume you can trade at one tick above the low of the range.
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Re: Should I use margin to buy a balanced fund?

Post by in_reality »

Day9 wrote:
Rob Bertram wrote:When it comes to the treasury defaulting, I'll fall back to what Larry Swedroe says: "it is as close to impossible as you can get and thus IMO should be treated as if it was. If that happens there are far worse problems anyway."
While that is true, the price could still fluctuate because of changes in perceived default risk.
Obviously I don't think the treasury will default long term either, and if it did, Larry would be right about there being far worse problems.

What happens though if the treasury doesn't have cash to pay interest payments in the short run. Delayed interest payment on $30 billion in interest payments is trivial in the grand scheme of US debt, but what would that do to treasury pricing?
the real test could come November 16 when the government is supposed to make some $30 billion in interest payments. It's predicted if the debt ceiling's not increased, the government will run out of cash somewhere between November 10 and 19. Though pinpointing that moment is not easy.
So are you assuming that you will have enough to avoid a margin call if the market goes to chaos for a while while things get sorted out. Are you assuming that the debt interest will get paid ahead of Federal Salaries?

I don't think that because things will get sorted out, that you can assume you will be able to stay liquid while they do. I think your plan should evaluate this risk.

I am not worried about Nov 16th. I think a leveraged plan using treasuries should not make assumptions that they will be fine. In a roiled market from the dept. ceiling not being raised both equities and treasuries might get shorted and sold and drop. Are you OK?

Sorry to say this but we are likely looking at this being a possibility every time the ceiling needs to be raised. Elections happen you know and who knows who will get voted in.

EDIT: NEVERMIND -- seems a two year deal is in the works... would keep it in mind though...
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Re: Should I use margin to buy a balanced fund?

Post by Rob Bertram »

HomerJ wrote:
Rob Bertram wrote:I was a little surprised to see the following success rates for 2006:
1-day: 91.9%
3-day: 96.1%
2-weeks: 97.1%
4-weeks: 97.4%
6-weeks: 98.4%
8-weeks: 98.7%
How much do you lose if (when) the 8-weeks 1.3% chance comes up?
This is a very important question, and the context is tricky. If we define the benchmark as a buy and hold 2-year treasury fund, then this strategy triggers when yields increase and the fund drops in value. A "success" for the bet would be to buy at the new low price and then sell after a short period of appreciation or dividend accrual. The net result of a successful bet is that the gain offsets the original loss.

So what happens to that 1.3% where the bet is not successful after 8 weeks? I am still money ahead of the buy and hold benchmark but not fully back to the original balance before the rate increase. So a "loss" is relative. It is correct to say that I did not gain the target amount, but I am money ahead of doing nothing.
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Re: Market timing 2-year treasuries using Martingale-style bets

Post by Rob Bertram »

market timer wrote:Are you assuming that if the 2-year futures trade at some level intraday that you are guaranteed the ability to trade at that level? This is potentially problematic. To be safe, I think you should assume you can trade at one tick above the low of the range.
I have been re-evaluating the model that I was using to calculate my betting success rate. It was assuming that I could buy at the intraday low and sell at a future intraday high. I agree that I should remove a tick from the low and possibly the high.

Another thing that I was doing was taking the prior day's close and comparing it to today's low to see if there was a price drop. I believe that I should change that. My main strategy is that I have a buy-and-hold (and roll) portfolio. There is a good chance that I opened my position weeks or months prior. So I shouldn't assume yesterday's close as my cost basis. In addition, my strategy's goal is to lower my cost basis to the current day's low if it is lower than my original basis. With those two things in mind, I am altering the model to assume my basis is the prior 2-week low +1 tick.

For 2006, this changes the success rates to
1-day: 99.0% (308/311)
3-day: 99.4% (309/311)
2-weeks: 99.4% (309/311)
4-weeks: 99.7% (310/311)
6-weeks: 99.7% (310/311)
8-weeks: 99.7% (310/311)
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Re: Market timing 2-year treasuries using Martingale-style bets

Post by lee1026 »

For things that are as far out as 2 weeks, how you model the roll will start becoming extremely important.

As an aside, if you think this will work, the correct answer isn't to try to lower your "cost basis" but to simply make money buying the dips and then selling a few ticks over.
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