Optimal portfolio and spending rules for endowment funds

We investigate the role of different spending rules in a dynamic asset allocation model for university endowment funds. In particular, we consider the fixed consumption-wealth ratio (CW) rule and the hybrid rule which smoothes spending over time. We derive the optimal portfolios under these two strategies and compare them with a theoretically optimal (Merton) strategy. We show that the optimal portfolio with habit is less risky compared to the optimal portfolio without habit. A calibrated numerical analysis on U.S. data shows, similarly, that the optimal portfolio under the hybrid strategy is less risky than the optimal portfolios under both the CW and the classical Merton strategies, in typical market conditions. Our numerical analysis also shows that spending under the hybrid strategy is less volatile than the other strategies. Thus, endowments following the hybrid spending rule use asset allocation to protect spending. However, in terms of the endowment’s wealth, the hybrid strategy comparatively outperforms the conventional Merton and CW strategies when the market is highly volatile but under-performs them when there is strong stock market growth and low volatility. Overall, the hybrid strategy is effective in terms of stability of spending and intergenerational equity because, even if it allows short-term fluctuation in spending, it ensures greater stability in the long run

The role of longevity bonds in optimal portfolios

We study the optimal consumption and portfolio for an agent maximizing the expected utility of his intertemporal consumption in a financial market with: (i) a riskless asset, (ii) a stock, (iii) a bond as a derivative on the stochastic interest rate, and (iv) a longevity bond whose coupons are proportional to the population (stochastic) survival rate. With a force of mortality instantaneously uncorrelated with the interest rate (but not necessarily independent), we demonstrate that the wealth invested in the longevity bond must be taken from the ordinary bond and the riskless asset proportionally to the duration of the two bonds. This result is valid for both a complete and an incomplete financial market

Investment Strategies in Incomplete Markets: Sufficient Conditions for a Closed Form Solution

This paper analyses the portfolio problem of an investor who wants to maximize the expected power utility of his terminal wealth both in a complete and an incomplete financial market. We derive sufficient conditions for having a closed form solution. These conditions must hold on a suitable combination of the drift and diffusion coefficients of the stochastic processes describing the state variables and the asset prices. In particular, we show that our framework leads to two cases: (i) the case solvable thorough a log-linear value function, and (ii) the case solvable thorough a log-quadratic value function