# A Logic Riddle (Heads You Lose, Tails You Lose), from Rocky Humbert

November 8, 2011 |

Real interest rates are back near their recent record lows (5 year TIP= negative 1.2%; 10 Year TIP= negative 0.15%); and gold's recent behavior is once again consistent with these facts. Riddle me this, Batman:

If I buy a 5-year TIP at a negative 1.2% real yield, and hold it to maturity, that means I am certain to lose 1.2% of purchasing power over the next five years. BUT: Were I instead to short a 5-year TIP at a negative 1.2% yield, and hold the short to maturity, does that mean I am certain to make 1.2% of purchasing power over the next five years? And, how can BOTH of these statements be false?

Private riddle for The Chair:

What do Galton, Batman, and Robin have in common?

The Riddler's False Notion:

Robin: Holy molars! Am I ever glad I take good care of my teeth!

Batman: True. You owe your life to dental hygiene.

## Sushil Kedia writes:

Logic Riddle is a misnomer for what is truly a contradiction. The presentation has a contradiction. In life, in markets there are no contradictions. Allow me to quote Ayn Rand from the Atlas Shrugged, "If there is a contradiction, check your premise".

Rocky, your logic is based on inflation remaining what it is right now the same also during the maturity and at the point of maturity of the 5 year TIPS! Market is not pricing that! Market is pricing inflation will come down! That's all. Check the premise, there are no contradictions.

Purchasing Power is a good term to help create this contradiction. Purchasing power will be Cash in your hand on day of maturity Divided by (1+inflation)^5 if I take the Annualized realized inflation readings. Realized Inflation readings five years from now will be known only then.

## Rocky Humbert responds:

Dear MisterMeanor:

2. That means it's possible to have not only a negative REAL YIELD but it's also possible to have a negative NOMINAL RETURN! (So much for the risk-less treasury market.

4. Your statement "Market is pricing inflation will come down! That's all. Check the premise, there are no contradictions" is 100% UPSIDE DOWN. There is little justification for locking in a negative 1.2% compounded real yield UNLESS you have no alternative investment that does better. You need an inflation assumption of RISING INFLATION not falling inflation due to the way these seasoned bonds behave.

I reckon, back of the envelope, north of 3.8% compounded CPI…. is required to have these TIPS beat the bullet 5 year … and even then you still lose 1.2% of purchasing power (compounded) per year. If you want to bet on disinflation/deflation, you would short these bonds at 105 with an inflation factor of 226/220 with abandon, and buy 5 year bullet bonds to term.

Batman just ended. The Flintstones are on now.

## Charles Pennington writes:

That's a very nice riddle.

These bonds trade dearly I think because there aren't many other competing foolproof CPI inflation hedges.

Obviously if you short the bonds AND hold the short sale proceeds in cash, you are at risk of losing money. You short \$1 million in bonds and hold the \$1 million proceeds in cash. The bonds could go up in nominal terms by a factor of ten to \$10 million. Meanwhile your short sale proceeds sit there in cash, still just \$1 million, and when you cover, you lose \$9 million. That's a loss in any terms.

Of course, if you could use your short sale proceeds to buy something that tracks the CPI without the built-in "negative carry" that the TIPS have, then you'd have a perfect arbitrage. But such a thing doesn't exist.

(Does it?)

A 1 year bond is four three month bonds.

A three month bond is a treasury bill financeable for cash as legally defined by the government at the rate set by the federal reserve.

If ex ante you knew that rate, let's say it would be zero for the next year, then if the one year note traded at 1 percent, there would be risk free arbitrage in buying the note (because the note is defined as acceptable collateral to get cash without exception at the overnight rate, it is perpetually fungible).

But all of this is true because arbitrage needs a unit that you're left with at the end, say for example cash, to make the calc.

I will not solve the last part of your riddle yet Rocky.

Let me ask, can the fair value of cash, the unit of account in arbitrage, which is merely the desire to lend known resources today for unknown future wants x years from now, change?

I don't want to lend at these rates.

I'd rather just have the money in the bank.

But if you know the money in the bank is guaranteed to earn zero shouldn't you buy the bonds and finance them at zero?

And if you know that the nominal bond is priced on the arbitrage condition above, and you believe that inflation will be three percent,t hen if you short the bond and earn the overnight rate risk free, and buy the tip and pay the over night rate risk free,and you hold these positions to maturity, since they are both fungible for cash, then you are guaranteed to earn the difference between future CPI and the ex ante break-even, which is an unknown variable free to take any value.

If you had an opinion on the future rate of inflation you could express that view only because of the other variable being priced to remove arb.And the riddle you speak of which seems to be, why would you commit ex ante to a negative real return can be answered by saying arbitrage of the other instruments demands that only the break-even and not the real rate is solved for by the buyers and sellers in the tips market.

Then What is the real rate set by? That is a very tricky question. The answer is in the above, but not obviously.

## Duncan Coker writes:

I believe selling the 5 year Tip and buying the 5 year bond would do better than 1.2% (anti negative real rate) and would actually capture the inflation rate of around 2%. Empirically if you convert them to zero coupon for calculations then sell the 5 year tip around 105, buy the 5 year bond at 95, this makes for a compounded return of around 2%, 10 profit, holding to maturing. But then again there is a reason I don't trade bonds much.

I think of tips only in term of the real yield. It would take a very unusual set of circumstances to get me excited about investing in a situation where I can earn a negative real return. These bonds, if I recall all have CPI floors built into them so persistent deflation while sapping a bond of its built in inflation accretion can't turn the redemption figure below par. Each bond has a different sensitivity to the built up inflation component depending upon when issued. This is because the bond pays the same real coupon and the principal balance is adjusted by prior CPI (riding on a train so can't look up)

Certainly these bonds are one of the only high quality ways to hedge inflation. There are a number of global ways to do this but France, etc. Have bigger issues.

So what can happen when you short one of these. I wonder for those who can obtain info what the cost to borrow for the short is here. Obviously the overnight reinvestment is not a plus here.

Seems like I should expect to earn the real yield in this case which is a depreciation toward par but what is my short cost?

## Tyler McClellan responds:

I set up my example clearly.

The reason the thirty year bond cannot be arbitraged to short term rates is very simple. There is no way to credibly make the claim that short term rates will be X for thirty years. There is no institution that can impose the stick. I put very little weight on all the other things. Its the fact that short terms rates could be radically different in the future that generates the volatility not the other way around. Long bonds are very convex and thus this is a major reason they should have a lower yield, offsetting the term premium.

Your examples about LTCM and MF Global are meaningless. Their assets were never fungible at 100 percent leverage for the overnight rate. The Fed conducts monetary policy by making cash and bonds of certain maturities exchangeable for each other at certain overnight rates. To compare this to MF global where the bonds are explicitly not instantaneously fungible with cash (euros) is very odd.

Your example about RV strategies in fixed income is a good counterpoint to the limits of arbitrage. I agree that a one year rate 29 years forward is not subject to the same laws of arbitrage as other instruments. This is for a simple reason. The one year rate 29 years forward is not something that is dynamically set in the market by participants trading until equilibrium. It is an artifice of other things that are traded in this manner and thus it "falls out" of other asset prices.

In general arbitrage is the mechanism by which the sum of views in the market derive their equilibrium condition. You have to have a variable that reflects some view for arbitrage to do heavy lifting. I cannot arbitrage a one day interest rate 17.75 years forward for the simple fact that there are no views on that variable and thus it is merely an artifice that arises from the ecology of the market.

As for mingling "real and nominal". You do not understand your own analysis. The market already believes that we will have about 2% inflation and is nonetheless holding cash at 0%. So the accepting of negative real returns ex ante exists in many markets as a necessary fall out of accepting other variable. To say that this comes from the TIPS market is strange. All the tips market does is allow people to have differing views on the future rate of inflation. Everything else is determined by much more liquid (and therefore likely to be subject to arbitrage pricing) markets.

You will get negative real returns (your vaunted guaranteed decline in real wealth (a phrase that I dont understand)) ex ante in either the nominal or the TIPS market. If you reread what you wrote, you will understand this has nothing to do with TIPS.

As for your last question. You already understand the answer rocky. You get more than PAR day one for being short the TIP.

If you

1) take all those proceeds and reinvest them at the fed fund rate at the future path

2) and if inflation is equal to the breakeven-rate

3) then you will lose the real value of the capital lent to you at exactly the same rate that the market says the real value of the capital lent to you must go down ex ante.

Put another way,

If

1) you must earn the nominal return priced in the market,
2) experience the inflation rate priced into the market,
3) and deposit your funds at the monopoly price set by the FED,

then you are indifferent between the two outcomes and are guaranteed to earn the same negative return. Which is of course why there is a market. All of which i wrote a long time ago as a explanation for why it might make sense to be short tips but if an only if you could tell me why based on your estimate of the above three variables. Any speculation on the real rate is meaningless, it is not a variable one can have a view on outside of the above (if and this is a key assumption, cash money from the fed reserve is the unit of account you wish to sum all the steps across. Its very possible the real term structure of other commodities is different)

## Rocky Humbert responds:

I will address your many points more specifically when I have some time. But I will make a very simple observation (which you ignored)….which has to do with the interactions between inflation and tax policy and the zero interest rate boundary problem.

Let's assume a simple Taylor rule and that the fed sets overnight funds at inflation+100 basis points. Let's further assume a marginal tax rate of 30%.

Case I) Let's assume that inflation is running at 5%. Then fed funds is 6%. Then my after-tax nominal return = 0.7x 6% = 4.2% and my after-tax real return is negative 0.8%.

Case II) Let's assume that inflation is 2%. Then fed funds is 3%…and my after-tax nominal return = 0.7×3%= 2.1% and my after-tax real return is positive 0.1%.

Case III) Let's assume that inflation is NEGATIVE 2%. Then fed funds is 0% … and my after-tax nominal return = 0%, but my after-tax real return is positive 2%.

This is a clear example where real after tax returns behave in counter-intuitive ways…. and so the apparent negative return on TIPS might have less to do with inflation expectations per se, and more to do with the tax effects…. (or more succinctly, an investor in Case III above would be willing to buy a tip that has a negative 2% real yield and would be indifferent to case II, where the same TIP has a +100 real yield.) Just a thought

## Tyler McClellan writes:

Very true. I once worked with Paul McCulley on the tax implications of same. As you never posed that as a question I didn't address it.

I agree with your points and thing it is a modest contributor the the current equilibrium pricing.

## Philip J. McDonnell writes:

I think one point that has not really been made in this discussion is that TIPS are paid back at the greater of inflation adjusted value or par. This means that they have an implied deflation protector built in.

It is like a deflation put which has intrinsic value in and of itself. In many ways we are in a deflationary environment caused by the great credit bubble unwinding throughout the world economy.

I just scanned the riddle discussion. It seems to me that the reason you can't make money shorting TIPS is like the obviously idiotic action of shorting dollars in dollars. Let's say you decide to short a million dollars, and sell it to someone for a million. That's what shorting is, and yet you are in exactly the same situation as you once were.

If TIPs are losing purchasing power against a basket of commodities, but dollars are losing it faster, if you short TIPS you get something that loses purchasing power even faster than TIPS, hence no gain. If you could find a way to get paid for your shorted TIPS with a basket of commodities, and there is high inflation, you can buy them back with fewer commodities, so you make a profit.

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