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On the risk-free rate

Hooijman, T.H.J. (2016) On the risk-free rate.

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Abstract:Currently several governments receive money for borrowing up to seven years. This fundamentally contradicts with time preference implying that investors always require a positive return. Furthermore, it evokes questions about the functioning of the bond market, and about government bonds’ adequacy as proxy for the risk-free rate. Although government bonds were historically almost unquestionably used as risk-free rates, we formally disentangle the two concepts by defining a risk-free asset as theoretical concept and government bonds as estimators. This strict separation enables us to select the best estimators for the risk-free rate for valuation purposes. Firstly, we distinguish two methods to estimate the risk-free rate: proxies and models. Proxies are observable variables and estimate an unobservable variable by closely resembling it. Models consist of several variables together related by theory to the unobservable variable. We evaluate two risk-free proxies: German government bonds and Overnight Indexed Swaps. We discard two other proxies: General Collateralized Repurchase Agreements and our developed ‘Market-Implied Risk-Free Rate’, because they are not available for longterm maturities needed for valuations. Besides the proxies, we construct a ‘Macro Model’ by regressing macro-variables on the German government bond in a period it closely resembled a risk-free asset. We discard other models, because the Macro Model has historically the best explanatory power for riskfree proxies. Subsequently, we define three evaluation criteria for risk-free estimators: Consistency, Intelligibility and Availability. Firstly, we measure Consistency by comparing the risk-free estimators with a Market-Implied Risk-Free Rate, which we define as the market’s view of a risk-free portfolio. Secondly, we evaluate Intelligibility by comparing the resemblance of the estimators with a risk-free asset. Finally, we measure Availability as the publishing frequency of the estimators. Our aggregated analysis shows that the German government bond is the best risk-free estimator by performing as good as or better than the alternatives on all criteria. Afterwards, we analyze deficiencies of the German government bond as risk-free estimator and their causes. We show that credit risk, flights-to-liquidity, and Quantitative Easing programs all deviate the Bund from the risk-free rate. We propose adjustments for the former two and not for the latter, because our estimation of that deficiency is inaccurate. We propose using CDS to eliminate partially the credit risk exposure and using German agency bonds to partially eliminate the liquidity premium. Although our adjustments improve the Bund as risk-free estimator conceptually, the adjustments worsen the Consistency of the risk-free estimator. We attribute this to the neutralizing effect of the positive credit risk premium and the negative liquidity premium of the Bund. Concluding, we recommend to use German government bonds to estimate the risk-free rate. Finally, we reflect on theory stating that investors require a positive return and show it to be incorrect. We propose three reasons for the acceptance of negative returns: (i) speculation about bond price increases or currency appreciation, (ii) regulatory requirements for financial institutions, and (iii) lack of alternative assets. We think that all three factors push the lower bound of interest below zero. However, the question remains; “What is the lower bound?”
Item Type:Essay (Master)
PwC, Amsterdam, Netherlands
Faculty:BMS: Behavioural, Management and Social Sciences
Subject:83 economics
Programme:Industrial Engineering and Management MSc (60029)
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