Risk quantifcation of mixed portfolios containing bonds and stocks

Abstract

In this study, we design a method to quantify the expected return and risk of mixed portfolios containing bonds and stocks using the historical data and expert opinion about the future changes in the market. Vasicek model was the model we used as the short-rate model. Short-rate models are single factor models that give the possibility to price bonds with di erent time-to-maturities with a single random variable, the short-rate. We implemented the expert's expectation of future short-rate into Vasicek model to simulate future short-rates and developed a parameter calibration to obtain a yield curve closer to the current market yield curve. We used the lognormal multinormal model to simulate the future log-returns of the stocks. The design of a model for bonds and stock in a single portfolio requires information on the dependence between short-rate changes and bond returns. We calculated the empirical correlation between short-rate and stock returns for a large number of American stocks. The results showed that the empirical correlations were all close to zero. So we assumed that the changes of the short-rate and of the stock prices are independent. It is therefore not di cult to simulate many possible future portfolio values and to represent them in a histogram. It is also easy to use those simulated values to calculate the mean return and the risk measures VaR and CVaR of the portfolio.