Optimal Wealth Allocation to Interest-Bearing Central Bank Digital Currency in Investor Portfolios: A Merton Model Approach

Floating interest Central Bank Digital Currency (CBDC) is a moderately risky financial asset. Given the risks involved and the returns attached, a rational investor has to determine the optimal allocation of wealth to the CBDC in his or her portfolio. The paper sought to establish the optimal wealth allocation to a floating interest rate CBDC and a risk-free asset. The study adopted an analytical design to illustrate the theoretical optimal holding of floating interest rate CBDC by individual investors based on Merton's 1969 mathematical model. Using data collected from the Central Bank of Kenya and Kenya National Bureau of Statistics, the paper applied the Merton model to a hypothetical proxy for CBDC, and real-world data on inflation, interest, and 91-day T-bill, to allocate investors' wealth to floating interest CBDC and a risk-free asset. The results show that optimal wealth allocation to floating interest rate CBDC was a function of the risk premium, the degree of investor risk aversion and the volatility of the floating interest rate CBDC. The results further demonstrate that whenever CBDC offered a higher interest rate than a risk-free asset, investors would shift wealth to CBDC and vice versa. Further, whenever the volatility on CBDC returns increased, investors tended to hold fewer units of interest-bearing CBDCs and more of risk-free assets and vice versa. The optimal monthly consumption for the risk-averse investor was a function of subjective discounting rate, degree of investor risk aversion and previous wealth. A higher subjective discounting rate or a higher cumulative wealth, or a lower risk aversion was associated with increased optimal consumption, <i>ceteris paribus</i>, and vice versa is true. Our results therefore suggest that financial markets investment portfolios are sensitive to CBDC volatility, and this that can originate another strand of CBDCs literature. These findings provide useful insights to individual and institutional investors, and can guide policymakers and financial market regulators on the important link between CBDC and financial markets in the new digital-currency era. For example, policymakers and regulators can adjust fiscal and monetary policy by considering the possible impact on investor portfolios. This can guide investors to strategically adjust their portfolio positions.