The Free Exchange blog has a piece that tries to explain the recent moves in INR using the portfolio-balance effect of QE. I have been sceptical of portfolio balance.

Portfolio Balance

I am sceptical of analyses of the effects of QE that are based on the portfolio-balance idea, because I do not think it captures the most important transmission channels. Let us think about QE in two different ways, using two very simple models.

1.

Imagine a simple system in which a government issues 100 bonds in each period, all of the bonds are bought by four people, and the bonds are held to maturity. Each person is prepared to buy an exogenous number of bonds at a price up to an exogenous limit, and no bonds beyond that price (perhaps the people should have sloping demand curves, but it is not so unreasonable to think people will either buy as much as they want at a price they like, or none at a price they don’t; anyway, it is not so obviously silly as to make me reject this simple model). The people are:

Aethelstan
Boudica
Caesar
Diocletian

A new, price-insensitive buyer enters the market with a desire to buy 25 bonds. What will happen to the market price? It depends on the dispersion of the prices that the four existing players are prepared to pay. Imagine the following case:

Aethelstan 25 bonds @ 50
Boudica 25 bonds @ 40
Caesar 25 bonds @ 30
Diocletian 25 bonds @ 20

Without the price-insensitive buyer, the market-clearing price will be 20, because Diocletian will be the marginal buyer. With the price-insensitive buyer, the market price will rise to 30, because the marginal buyer will be Caesar.

Now imagine a second case:

Aethelstan 25 bonds @ 23
Boudica 25 bonds @ 22
Caesar 25 bonds @ 21
Diocletian 25 bonds @ 20

In this case, the entry of the price-insensitive buyer will cause the price to rise from 20 to 21.

We can see that the effect of the entry of a price-insensitive buyer will partly depend on the dispersion of prices that the other buyers are prepared to pay. I think that the bond market is probably more like the second case than the first — i.e., that the range of opinions among significant investors about what it would be reasonable to pay for bonds is likely to be relatively narrow. Thus, I think that changes in buyers’ collective assessments of value will usually be more important for explaining movements in bond prices than the entry and exit of buyers. This notion is supported by the fact that bond yields have tended to rise, not fall, during periods of QE (see figure 1). The portfolio-balance view omits changes in collective assessments of value.

QE and Bond Yield

Figure 1: US 5-year constant-maturity rate (LHS) and total assets of the Federal Reserve (RHS). Click to enlarge.

2.

How big an effect will the portfolio-balance channel have? Imagine that households wanted to move from bonds into emerging-market equities. Let us take it that these equities are presently held by foreigners. Households will sell their bonds, and this will indeed reduce the price. Let us assume that foreigners decide to buy them. Households spend exactly the proceeds from selling bonds to purchase EM equities (see figure 2).

Figure 2

Figure 2: Households sell bonds to purchase EM equities, while foreigners, attracted by the lower price, purchase bonds and, attracted by the bids from the households, sell some EM equities. Click to enlarge.

Now imagine that households want to move into emerging-market equities, and the central bank is willing to buy their bonds at the current market price. This means that the price does not fall when the bonds are sold. Households again purchase EM equities from foreigners. The amount expended on EM equities will be slightly larger than before, because the proceeds from the bond sale were larger (see figure 3).

Figure 3

Figure 3: Households sell bonds, through the banks, to the central bank. They use the proceeds to purchase EM equities from foreigners. Click to enlarge.

Let us compare the two cases shown in figures 2 and 3. The major effect on EM equities comes from the decision by households to purchase them by selling their bonds. QE has a marginal positive effect, because it makes the purchase of EM equities shown in figure 3 slightly larger than that shown in figure 2. However, it does not seem likely that this effect will be large enough to explain the strength of capital inflows into emerging markets in recent years, or why they should be reversing now.

US Interest Rates

If portfolio-balance does not seem likely to provide more than a marginal explanation, why else might asset prices be falling in emerging markets? Perhaps because US real interest rates have increased since Mr. Bernanke lit the touch-paper on tapering, causing real interest rates to rise. Higher real interest rates in the US ought to mean that the attraction of overseas assets to US investors is reduced, such that capital flows out of foreign markets and into the US.

If that was true, then one should expect changes in INR/USD to be related to changes in US real interest rates. That is something we can check out. Below is a chart (figure 4) that shows monthly changes in INR/USD and the US 5-year real interest rate (in blue) between June 2009 and April 2013 and a regression line (black; R-squared=0.22). The red points are daily rolling 20-day (i.e. about one month) changes from the start of May 2013 to today. There is an obvious moment of disconnection when the US real rate rose and INR/USD did not fall, but, looking at the time series chart (figure 5), it looks like INR/USD may just have taken a while to get going. The model does not appear to do a bad job of explaining the (out of sample) red points.

Figure 4

Figure 4: In-sample data (blue), out-of-sample data (red) and regression line. Click to enlarge.

Figure 5

Figure 5: Time series plot of INR/USD and US 5-year real interest rate (inverted). Click to enlarge.

Conclusion

It seems that it is not unreasonable to attribute the fall in INR/USD to the increase in real interest rates in the US, which in turn was the result of Mr. Bernanke’s comments on the subject of tapering.

One might explore this question further with a fuller model of the drivers of INR/USD. An obvious place to look would be a real interest rate differential between the US and India. However, because India does not have (to my knowledge) inflation-linked government bonds or inflation swaps (or at least liquid markets in them), real interest rate differentials cannot be calculated in the normal way. One might use actual inflation as a proxy for market-expected inflation, I suppose.

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