Which Is A Better Estimator Of Nigeria’s Risk Free Rate, the 364 Day T-Bill or the 10 Year Bond?

The other day while I was reading for my professional financial analysis examinations coming up next year, I came across the use of the 364 day T-bill rate as the assumed risk free rate in calculations of cost of capital and other calculations

This isn’t the first time I have seen this being used. As a matter of fact, I have noticed the use of the 364 day T-bill rate as the risk free rate and also the 10 year bond yield used as risk free rates in various, without any reasons being proffered as to why these rates were used.

Discussing with an acquaintance at one of the big 4 consulting firms, I asked which of the two rates (364 T-bill rate and the ten year bond yield rate) he would rather use in measuring Nigeria’s risk free rate and why. He replied stating that the 364 day T-bill rate was a better measure of the risk free rate as it was less volatile than the ten year bond rate.

Disregarding the volatility argument for the moment and assuming that the Nigerian 364 day T-bill rate is used as the risk free rate, current yields on the Nigerian 1 year instrument (15 Dec 2016) is 7.51%. Deducting Nigeria’s assumed country risk of 7% from the 364 day T-bill rate (our assumed risk free rate) of 7.51% gives a net return of 0.51%, 10 basis points lower than the American 12 month note (GB12.GOV) of 0.61%.

Questions might be raised as to why 7% is used as the value of Nigeria’s risk profile. Most international rating agencies employ 5% as Nigeria’s country risk. However, using Investopedia’s definition of country risk which states that “Country risk is a collection of risks associated with investing in a foreign country. These risks include political risk, exchange rate risk, economic risk, sovereign risk and transfer risk, which is the risk of capital being locked up or frozen by government action”, Nigeria’s county risk can be taken to have increased substantially. Consistent political risk (Boko Haram and the Biafra agitations), movement in parallel markets from N191 in January to its current rate of N300, falling stock market capitalisation (N11.24 trillion to N9.24 trillion within the year), increased inability of the Nigerian government at all tiers to service their obligations (non-payment of aviation bill at the federal level and outstanding workers’ wages at the state are cases in point) currently plague Nigeria. This coupled with falling oil prices (OPEC basket moved from $51.78 To $31.15) and thus reducing external reserves ($34.494 billion to $29.34 billion) with strict restrictions on the use and transfer of foreign currency and an almost certain dip into recession point to an increasing country risk which for the purpose of this paper was therefore taken to be 7%.

The average investor will not put his funds in an investment wherein he is guaranteed to make a loss or lower profits (Nigeria’s net risk free rate, using the 364 day T-bill, being lower than America’s 12 month note is a perfect example) and would rather exit that investment as soon as possible or not go into it in the first place. While there has been a spate of withdrawals from the Nigerian economy by foreign portfolio investors (indeed these withdrawals may have been larger but for the restrictions on transfer of funds), however it has not been sufficient enough to point to a total abandonment of the Nigerian economy by foreign investors, this points to the fact that investors have intrinsically and subconsciously priced the risk –free rate above the current T-bill rate of 7.51%. This in fact is my major argument in supporting the use of the 10 year bond rate for measuring Nigeria’s risk free rate.

Going back to the initial argument of volatility and the 10 year bond being more volatile than the 364 day T-bill rate I computed the daily rate of returns for 2015 for both the 364 day paper and the 10 year bond and using their standard deviations as a measure of their volatility. Using the 14.20% 14 Mar 2024 bond as our 10 year paper and taking the oldest T-bill issue for each working day as our 364 day paper, standard deviation on the 364 day rate was 0.0644 while that of the 10 year bond was 0.0205. Over the last year the 364 day paper has proven to be more volatile than the 10 year bond, proving that in Nigeria’s current economic climate, the 10 year bond is a better measure of her risk free rate than the 364 day T-bill paper.

Taking excerpts from a mail with a colleague of mine, Louis Olabalu as my conclusion, the conditions that make an instrument risk free and secondly the factors that affect the basis of performance of such instruments are as follows:


1. No risk of default associated with its cash flow

2. No reinvestment Risk

Factors that determine basis of performance.

T-bills: — 1. Demand 2. Supply 3. Economic conditions 4. Monetary policy 5. Inflation rate

Bonds: — 1. Recession 2.savings 3.default likelihood 4.growth prospects 5. Inflation

They are both practically affected by both factor and meet the conditions. Without going into much details and analysis, the only determining factor to determine priority of use as risk free capital has to be the current state of the economy, likelihood of change of this current state in the nearest future and the analysis of the numbers of both instrument in the past months.

Based on this current state of the economy and the likelihood of change in the nearest future, I will support bonds as a basis for risk free rate

at this time and also factored on what we will resolve from the analysis of the figures.

T-bills would have been the priority, if the current state of the Nigerian economy was encouraging

First published on Linkedin Pulse, December 27 2015.

All opinions expressed are strictly those of the author and are not necessarily the view of any institution, organisation or body he may be affiliated with.