Portfolio management with stochastic interest rates and inflation ambiguity

Abstract

We solve a stock-bond-cash portfolio choice problem for a risk-and ambiguityaverse investor in a setting where the inflation rate and interest rates are stochastic. The expected inflation rate is unobservable, but the investor may learn about it from realized inflation and observed stock and bond prices. The investor is aware that his model for the observed inflation is potentially misspecified, and he seeks an investment strategy that maximizes his expected utility from real terminal wealth and is also robust to inflation model misspecification. We solve the corresponding robust Hamilton-Jacobi-Bellman equation in closed form and derive and illustrate a number of interesting properties of the solution. For example, ambiguity aversion affects the optimal portfolio through the correlation of price level with the stock index, a bond, and the expected inflation rate. Furthermore, unlike other settings with model ambiguity, the optimal portfolio weights are not always decreasing in the degree of ambiguity aversion.

Portfolio choice with stochastic interest rates and learning about stock return predictability

“…This, in turn, implies that getting a better estimate for the expected stock return matters less and the loss from ignoring learning becomes smaller. Similar findings were reported by Flor and Larsen (2014), Branger et al (2013), and Munk and Rubtsov (2014).…”

“…Furthermore, we demonstrate that learning about the unobserved component of the expected stock 1 Modelling an ambiguous investor is beyond the scope of this paper. However, according to the studies of Maenhout (2006), Branger et al (2013), Flor and Larsen (2014), Munk and Rubtsov (2014) among others, who also consider a setting with stochastic investment opportunities, ambiguity about traded assets usually results in less aggressive trading strategies, significant utility losses when ambiguity is ignored, and an additional hedge term appearing in the optimal portfolio. Thus, we expect ambiguity to have similar effects, if modelled in the context of our model, without changing the main findings of our paper.…”

“…To keep similar notation for value functions, let us denoteṽ (i) (t, x, y) := w(t, x, y;φ (i) ). Following Branger M A N U S C R I P T ACCEPTED MANUSCRIPT et al (2013) and Munk and Rubtsov (2014) …”

Robust portfolio choice with derivative trading under stochastic volatility

“…11 7 Different formulations of robust control problems and their comparison are discussed in Trojani and Vanini (2004) and Hansen and Sargent (2006). 8 This assumption was also made in Maenhout (2004), , Flor and Larsen (2014) and Munk and Rubtsov (2014), among others. For a critique of this approach, see Pathak (2002).…”

“…Flor and Larsen (2014) consider an investor who is ambiguous about the models for the interest rate and stock returns. Munk and Rubtsov (2014) study the impact of ambiguity about expected inflation on the choice of portfolio.…”