The intrinsic interest rate equation: \(\text{Intrinsic Riskfree Rate = Inflation + Real GDP Growth}\) can be used to both explain why interest rates vary across currencies as well as variation in exchange rates over time. If we accept the proposition that the interest rate in a currency is the sum of the expected inflation in that currency and a real interest that stands in for real growth, it follows that risk free rates will vary across currencies. Getting those currency-specific risk rates can range from trivial (looking up a government bond rate) to difficult (where the government bond rate provides a starting point, but needs cleaning up) to complex (where we have to construct a risk free rate out of what seems like thin air).
There are a few dozen governments that issue ten-year bonds in their local currencies, and the search for risk free rates starts there. We can then compute a risk free rate by netting out the default spread:
\[\text{Riskfree Rate in currency = Government bond rate – Default Spread for sovereign local - currency rating}\] Note that the Riskfree Rate in currency is only as good as the three data inputs that go into them. First, the government bond rates reported have to reflect a traded and liquid bond. Second, the local currency rating is a good measure of the default risk, a challenge when ratings agencies are biased or late in adjusting. Third, the default spread, given the ratings class, is estimated without bias and reflects the market at the time of the assessment.
If we have doubts about one or more of three assumptions needed to use the government-bond approach to getting to risk free rates, there is an alternative called the synthetic risk free rate. This approach can be used in almost any setting to estimate a local currency risk free rate, including currencies with no government bonds outstanding, where the government bond rate is not trustworthy, and pegged currencies.
In the table above, we start with a currency in which we feel comfortable estimating a risk free rate, say the US dollar. If the key driver of risk free rates is expected inflation, the risk free rate in any other currency can be estimated using the differential inflation between that currency and the US dollar.
\[\text{Local Currency Risk Free Rate} = (1 + \text{US RiskFree Rate}) \frac{(1+\text{Inflation Rate in local currency})}{(1+\text{Inflation Rate in US})}-1\]
The key inputs here are the expected inflation rate in the US dollar and the expected inflation rate in the local currency. The former can be obtained from market data, using the difference between the US T.Bond rate (DGS10) and the TIPs rate (DFII10), but the latter is more difficult.
While we can always use last year’s inflation rate, but that number is not only backward looking but subject to manipulation, I prefer the forecasts of inflation that we can get from the IMF (PCPIPCH):
DGS10: 10-Year Treasury Constant Maturity Rate
DFII10: 10-Year Treasury Inflation-Indexed Security, Constant Maturity
TIE: Treasury-based Inflation Expectation: The difference between the DGS10 and the DFII10 is a measure of expected inflation.
MICH: University of Michigan: Inflation Expectation Survey. Median expected price change next 12 months.
STLPPM: The Price Pressures Measure is the probability that the expected personal consumption expenditures price index (PCEPI) inflation rate (12-month percent changes) over the next 12 months will exceed 2.5 percent.
To summarize:
With high inflation currencies, the damage wrought by the higher interest rates that they bring into the valuation process are offset by the higher nominal growth we will have in the cash flows, and the effects will cancel out.
With low inflation currencies, any benefits we get from the lower interest rates that come with them will be given back when we use the lower nominal growth rates that go with them.