Most risk and return models in finance start off with an asset that is defined as risk free and use the expected return on that asset as the risk free rate. The expected returns on risky investments are then measured relative to the risk free rate, with the risk creating an expected risk premium that is added on to the risk free rate. But what makes an asset risk free? And what do we do when we cannot find such an asset? An asset is risk free if we know the expected returns on it with certainty – i.e. the actual return is always equal to the expected return. But an important question is under what conditions will the actual returns on an investment be equal to the expected returns? In order to answer this question, one has to look at two basic conditions that have to be met.

The first is that there can be no default risk. Essentially, this rules out any security issued by a private firm, since even the largest and safest firms have some measure of ** default risk**. The only securities that have a chance of being risk free are

**, not because governments are better run than corporations, but because they control the printing of currency. At least in nominal terms, they should be able to fulfill their promises. Even though this assumption is straightforward, it does not always hold, especially when governments (especially in emerging markets) refuse to honor claims made by previous regimes and when they borrow in currencies other than their own. These assumptions are based on the fact that government does not default in local borrowing and also does not borrow long term locally. But there are emerging markets and even developed markets where it is feared that this assumption does/will not hold.**

__government securities__

There is a second condition that riskless securities need to fulfill that is often forgotten. For an investment to have an actual return equal to its expected return there can be no ** reinvestment risk.** To illustrate this point, assume that you are trying to estimate the expected return over a five-year period and that you want a risk free rate. For example, a six-month Treasury bill rate, while default free, will not be risk free, because there is the reinvestment risk of not knowing what the Treasury bill rate will be in six months. Even a 5-year treasury bond is not risk free, since the coupons on the bond will be reinvested at rates that cannot be predicted today. The risk free rate for a five-year time horizon has to be the expected return on a default-free (government) five-year zero coupon bond. This clearly has painful implications for anyone doing corporate finance or valuation, where expected returns often have to be estimated for periods ranging from one to ten years. A purist’s view of risk free rates would then require different risk free rates for each period and different expected return.

Therefore, governments in these markets are viewed as capable of defaulting in local borrowing, even in some developed markets. For example Greece 2 year bond yield is 347% (24th July 2012) compared to German bond of same duration that has a negative bond yield of -0.056%, (that means in Germany, instead of paying to loan out your money, you pay them to hold your money). For Greece, it means that investors are unwilling to buy the bond because they believe they will not get their investment back when the bond is due to pay back the principal. Greek bond buyers are buying lottery tickets essentially. So why would investors not buy the Greece bond like the German bond? Is it not backed by same sovereignty power that made them risk-free assets? The reason is for flight to quality or safety or risk off. People are so scared of investing to lose so they prefer to have a guaranteed small loss than possible high loss by investing in something else.

Another reason in this particular example is that if you buy German bond what currency will you be paid in if they leave the euro zone as is likely? A new Deutsche Mark would dramatically appreciate (at least for a short time) right after its release. If you hold one of the German bonds you would make a huge return in the currency fluctuations.

However, to overcome this challenge, experts believe that in estimating the risk free rate, you look at and compare the rate at which big and safe local corporations borrow and use it as a base. But these firms no matter how safe they seem default. So it is believed that a rate marginally lower than this rate should be used. You can also use interest rate parity and Treasury bond rate in any other base currency to arrive at the local borrowing rate, provided there are long-term forward dollar-denominated contracts in the currency. However, the biggest limitation to this approach is that getting the forward rate for transactions beyond year 4 is very difficult in emerging markets. You can also arrive at the rate by getting the local government default spread. This could be gotten through the country’s currency rating. For example, if Nigeria’s default rate is 2% and the currency’s rating is A i.e. 10%, the riskless rate is 8%. Riskless rate = Government bond rate – default rate.

Under conditions of high and unstable inflation, valuation is often done in real terms. Effectively, this means that cash flows are estimated using real growth rates and without allowing for the growth that comes from price inflation. To be consistent, the discount rates used in these cases have to be real discount rates. To get a real expected rate of return, we need to start with a real risk free rate. While government bills and bonds offer returns that are risk free in nominal terms, they are not risk free in real terms, since expected inflation can be volatile. The standard approach of subtracting an expected inflation rate from the nominal interest rate to arrive at a real risk free rate provides at best an estimate of the real risk free rate.

The risk free rate used to come up with expected returns should be measured consistently with how the cash flows are measured. Thus, if cash flows are estimated in nominal Naira terms, the risk free rate will be the Nigeria Treasury bond rate. This also implies that it is not where a project or firm is domiciled that determines the choice of a risk free rate, but the currency in which the cash flows on the project or firm are estimated. Thus, Oando plc can be valued using cash flows estimated in Naira, discounted back at an expected return estimated using Nigerian long term government bond rate or it can be valued in British pounds, with both the cash flows and the risk free rate being the British pound rates. Given that the same project or firm can be valued in different currencies; will the final results always be consistent? If we assume purchasing power parity then differences in interest rates reflect differences in expected inflation rates. Both the cash flows and the discount rate are affected by expected inflation; thus, a low discount rate arising from a low risk free rate will be exactly offset by a decline in expected nominal growth rates for cash flows and the value will remain unchanged. If the difference in interest rates across two currencies does not adequately reflect the difference in expected inflation in these currencies, the values obtained using the different currencies can be different. In particular, projects and assets will be valued more highly when the currency used is the one with low interest rates relative to inflation. The risk, however, is that the interest rates will have to rise at some point to correct for this divergence, at which point the values will also converge.

Be that as it may, the most important thing for investor is to realize that for an investment to be worthwhile, (if the investment objective is majorly on good return) the expected return should be above the risk free rate, especially when one is investing outside the risk free assets.

*By Idika Aja*