# How to determine risk-free rate of Ecuador?

I have a question in determining the risk-free rate of Ecuador. For developed countries like United States and Great Britain, the risk-free rate can be obtained in financial database such as Reuter or Bloomberg by directly obtaining the government bond/bills yields or swap rate curve.

However, for developing countries such as Ecuador, I cannot obtain the risk-free rate based on Reuter or Bloomberg. As a result, how is its risk-free rate determined?

• The risk free rate is determined by demand & supply, which, combined with no arbitrage, leads to the Fisher parity – Julian Lopez Baasch Dec 19 '13 at 17:39
• However, for Ecuador, the currency used is United States, then I simply adopt US treasury bonds/bill yields as risk-free rate? But I feel strange about using US treasury bonds/bill yields as risk-free rate. If the US rate can be used as proxy of Ecuador risk-free rate, what is the rationale? – Dennis Dec 19 '13 at 17:51
• I mean, there can not be TWO different risk free rates in the same world... – Julian Lopez Baasch Dec 19 '13 at 17:56
• If there cannot be two different risk free rates, then how the risk-free rate of Ecuador is determined? Since the currency of Ecuador is US Dollar, then I can only use US related currency to determine the risk-free rate, which is the same as determining the US risk-free rate. Then it makes me think that US risk-free rate is the risk-free of Ecuador. But it seems strange and I want to know how is the risk-free rate of Ecuador is determined exactly. Thanks. – Dennis Dec 19 '13 at 18:02
• @JulianLopezBaasch Of course there can be two different risk-free rates, if they are in different currencies. Here "risk free" generally means that the payment (i.e. receipt of the notional in a zero coupon bond transaction) is certain. The risk-free USD rate and the risk-free GBP rate can (and generally do) differ because they incorporate expected exchange rate movements (or if you prefer not to speak in terms of expectations, they incorporate the forward exchange rate). – Chris Taylor Dec 22 '16 at 11:08

Since Ecuador uses the US dollar, the appropriate rate to use for discounting is the US dollar risk-free rate (i.e. the zero coupon rate bootstrapped from the overnight swap curve). The US dollar is the natural numeraire to use for valuing securities priced in US dollars.

For example, say that Ecuador five year notes with a coupon of 10.75% are currently trading at par, and the US discount curve is flat at $r = 2$%. Then by discounting under the risk-free rate, we see that the price would be

$$\141.12 = \100 \times \exp(-5r) + \10.75 \times \sum_{t=1}^5 \exp(-tr)$$

The actual price of \$100 is obtained by discounting by the yield, which is about 10.21% (assuming the Ecuadorean yield curve is flat as well). The difference between the risk-free rate and the actual yield is the credit spread, which for Ecuador is 10.21% - 2% = 8.21%.

This highlights a subtlety - although the relevant risk free rate is 2%, we do not reproduce the traded prices for Ecuadorean bonds by discounting at the risk free rate, because the market does not consider Ecuadorean bonds to be risk-free.

In recent times, very few (if any) government bonds are actually considered to be risk free, which raises the question of what rate to use for the risk-free rate in any country! In practice, the risk-free rate is taken from the overnight swap curve, and other rates are generally at a premium to this. For example, the US 10Y redemption yield is currently priced around 0.15% above the risk-free rate, reflecting the market's valuation of the credit risk in US government bonds.

The risk free rate is not determined by the currency in use but rather by the credit worthiness of the issuer. As in Zimbabwe which has a bad track record of hyperinflation, but uses the USD, it comes down your expectation of being paid. For example Zimbabwe Treasury Bills for 2018 maturity are trading at 17c in the dollar, indicating what investors feel the worth is in two years time. Though in theory the interest rate on these bonds would indicate the risk free rate, it clearly in this case has no bearing on the risk itself if a Government is seen as potentially not paying. A good guide would be in the currency itself. If the USD is available on demand and foreign payments can be made without hindrance the rate will tend closer to the interest rate on Government bonds, however if there is a rate of more than 1:1 on the "local USD" then it would imply an additional risk to acknowledge. One would have to speak to a local to garner such detail.