Archive | July 2012

# Negative Real Interest Rates

According to John Hempton, China’s savers are forced to save at a negative real interest rate. With US treasuries and German Bunds also below inflation, a commentator writes:

Also, that in an era of negative rates, everyone will essentially lever up as much as they can and as far out on the yield curve as possible (issuing zero coupons, ideally), and that this should always be able to soak up the excess supply of cash?

The argument for believing that they are impossible is to consider the behaviour of a commercial entity, say, Apple. Suppose that you could borrow at a negative real interest rate, then you could issue 7 year bonds at a negative real interest rate. Now presuming that you could find any assets with a nominal yield, and a maturity at the same length as your issue. So you could, say issue a bond with a maturity dated to some old US treasury that was not a coupon, and buy that. In fact, there is no price that is too high for a bond offering free money, so the bond prices for coupon paying treasuries would go to infinity.

There are many reasons to believe that the above argument is flawed. Firstly, negative real interest rates does not mean zero coupon. Moreover, who would buy a zero coupon bond? We call that cash(!). Anytime that you see a zero coupon bond being bought, it is clear that the bond has an alternative use which is valuable to the buyer. (In this case it is a repo-able collateral for the banking sector). Secondly, when macro-economists talk about interest rates they mean the fed funds rate, but very few entities can actually borrow at that rate. Thirdly, even if you could engage in the carry trade outlines above, it has an unknown opportunity cost: there may be a profitable opportunity about to come up, so even if you can borrow money at negative real rates, it might be best to do so and simply keep that money against a rainy day. If you were google, and could borrow for thirty years at one or two percent, it is almost certainly right to simply borrow that money, and wait for an opportunity to invest it.

So perhaps the above discussion has offered some useful insights:

(1) A commercial company will never be able to borrow at zero coupon.

(2) If a government bond is selling at zero coupon, it is a sign of sickness in the interbank lending markets.

(3) Negative real interest rates are bounded by inflation.

(4) Given the low levels of inflation currently predicted in the TIPS market in the US, UK, and Germany, and typical spreads on commercial bonds compared to government bonds, it is likely that there are very few commercial entities that will be able to borrow at a negative real interest rate unless there is a significant rise in inflation.

(5) High inflation makes negative real rates for a commercial enterprise possible, but it will not occur at zero coupon, and so there will be a lack of obvious carry trade opportunities (Everything higher yielding will carry more risk, exactly as it should).

One will not that I have not mentioned dividend paying shares. It is often assumed that the stock market is inflation protected, and on balance this may be true, but because of wild swings in price, it is not without risk. However, it is probably true that a company that can borrow at less than its dividend yield, could borrow and buy back its own shares, and add value. However, this is always the case. And few companies seem to do it. For one thing, bond holders get worried if the debt to equity ration is high, and hence even if you can borrow at less than dividend, you can only borrow a finite amount of money, and there is an opportunity cost associated with it. Also, dividends can be cut if the company runs into difficulties, but it is more difficult to renege on bonds. (It should be self evident that you have won on this trade only if dividend yields stay above bond yields over the whole maturity of the bond). All in all, its a risky strategy. If you are in a sufficiently strong position to attempt it, you are probably better to pay out of your cash reserves and maintaining the option to raise cheap bonds if you need them.

# Is debt important?

Recently, on Zerohedge.com, I saw the following chart:

with the usual Zero hedge commentary about how debt will be the death of the US economy. It strikes me that their commentary was exactly wrong. This graph demonstrates monetary policy working exactly as it should: The fed funds rate was decreased and so there were more profitable opportunities at the margin, and people took on debt to finance them. If we look at the fed funds rate it does indeed decrease (on average) during this period.

I essentially believe in the market monetarist argument, that by controlling the price of money, via interest rates, the central bank controls the path of aggregate demand. The Fed, under Greenspan, used this to produce `the great moderation’, effectively through NGDP targeting, as when RGDP growth is stable, inflation targeting is indistinguishable from NGDP targeting.

It follows then, that the central bank controls aggregate demand by controlling the fed funds rate, which controls the total amount of debt. Following the end of Bretton woods in the early seventies, and the move to true fiat currencies, the US has had a much stabler NGDP path, this is the power of a fiat currency to regulate demand.

This brings us back, at last, to the question which began this post. Does debt matter? Krugman argues that money an economy owes to itself can never matter from a macro economics stand point. Scott Sumner has argued that debt is largely indistinguishable from money, and the NGDP is the appropriate measure of monetary policy, and hence that if NGDP is kept on track, the amount of debt will look after itself.

I propose a different understanding. During the great moderation, it seems to me that the central bank could, through quantiative easing, put NGDP on track, regardless of the funds rate. Lending is essentially money creation. Any asset that can be traded for money quickly (i.e. is liquid) is money. By lowering the feds fund rate, suddenly activities that were not profitable compared to cash in a bank account, become profitable, and through lending the money supply expands. Suppose instead that the central bank simply bought equities with newly created cash. This would expand the money supply, but since lending is based on the profitability of opportunities, it will not increase lending. It seems obvious that this would be expansionary monetary policy, with no associated expansion in debt.

It seems that monetary policy is a more subtle instrument than I had believed, and that it can simultaneously control both the path of aggregate demand, and the path of debt. In follow up posts I will explore this topic further. I also wish to explore the following questions:

(1) It seems to me that increasing the amount of debt necessitates rising inequality, since someone must be holding the savings that are being lent out. Is it possible that we have misdiagnosed the rise of inequality in developed nations, and that they are a symptom of monetary policy. This would certainly explain why the trends are so widespread, occurring at the same rate in close to every industrialised countries, even those with highly redistributive tax systems.

(2) While debt is roughly money, it exists on a sliding scale. In particular, changes in the likelihood of repayment can change the price of these assets. Since these are the money supply, is it possible that at some stage a change in price level can be sufficient to cause a significant contraction in the money supply, at least as avaiable to financial institutions. I have in mind the triple A rated securities formed from CDO’s. This was a market worth over a trillion dollars at its height. Happily exchanged via repurchase agreements at face value, they were, to all intensive purposes, interest bearing money. Almost overnight the market collapsed. A trillion dollars of money suddenly ceased to be money. To put that in perspective, that is more than the size of the US monetary base (i.e. cash). It would not surprise me in the least if this was found to be the proximate cause of the collapse in NGDP.

(3) If extra debt, through through price fluctuations, and solvency worries, can have non trivial influences on NGDP, it stands to reason that debt does add to systemic risk, and a central bank should use its power to print hard money, and buy debt, in order to prevent the ration of M3:M0 from growing inevitably. Essentially the conclusion that I have come to is to say that perhaps, even in good times, central banks should prefer quantitative easing to changes in the interest rate, in order to keep control of both aggregate demand and the level of debt simultaneously.

# Puzzle No 1: Cool Eggs

I like Puzzles, but its so hard to find good ones.

If an egg, initially at room temperature (20 degrees Celsius), is dropped into liquid nitrogen (-196 degrees Celsius), it takes approximately eight minutes to approach the temperature of the liquid nitrogen, if it is subsequently left out on a surface, it takes approximately 2 hours to return to room temperature. Why is the heating and cooling asymmetric?

So the essence of this problem is to identify, from among the various features, the one that dominates. Nearly everyone, when first given this question, comes up with the following answer:

The Air-Egg boundary transfers heat worse than the Air-liquid nitrogen boundary.

This is plausible, it is a well known fact that water conducts heat around twenty five times better than air. In practice, because the liquid nitrogen vaporises on contact, the egg is suspended in a bath of nitrogen vapour, which probably leaves the heat transfer properties similar to, or even worse than, that of an egg in air. It is very hard to know the exact consequences of this effect.

However, there is a second important effect:

Let us suppose that the coefficients of conduction are constant. In that case the rate of heat flow into the egg will be given, in both cases, by Newtons Law of cooling.

$\dot{Q} = \kappa A (T_{outside} - T_{surface})$

Obviously the area is also the same, for both eggs, so we can absorb the two constants into one. The dot stands for derivative, so the equation can be read: “The flow of heat is proportional to the temperature difference”. Now consider when the heat flows into the egg. The heat capacity of water is about four kilojoules per kilo per degree. The heat capacity of ice is about half that. However, the latent heat of freezing is about 330 kilojoules per kilo. Thus the total amount of heat flow needed is rougly

$196\cdot 2 + 330 +20\cdot 4 = 802 KJ$

Now consider, the act of melting/freezing. On the way up this happens with a temperature difference of 20 degrees, whereas on the way down this happened with a temperature difference of two hundred degrees. Thus it takes about ten times as long to melt as it did to freeze.

The solution to the law of cooling is

$t = - C\cdot\ln\left(\frac{\Delta T_{end}}{\Delta T_{start}}\right)$

, but this does not lend itself to an obvious solution, since it will never reach the temperature of the medium. This just shows the relative inaccuracy of this type of law. Suppose we measure the time taken to reach five degrees of the end points, then we can find that cooling takes about one third of the time to heating. So we conclude that the latent heat effect introduces a factor of about three, and transference effects introduce a factor of about six.

I find it interesting that even if the conduction coefficients were perfectly symmetrical, this process would still be asymettric.