On the Exact Solution of the Multi-Period Portfolio Choice Problem for an Exponential Utility under Return Predictability

In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint random process of the asset returns and the predictable variables follow a vector autoregressive process. We prove that the optimal portfolio weights depend on the covariance matrices of the next two periods and the conditional mean vector of the next period. The case without predictable variables and the case of independent asset returns are partial cases of our solution. Furthermore, we provide an empirical study where the cumulative empirical distribution function of the investor's wealth is calculated using the exact solution. It is compared with the investment strategy obtained under the additional assumption that the asset returns are independently distributed.Comment: 16 pages, 2 figure

Optimal Value and Growth Tilts in Long-Horizon Portfolios

We develop an analytical solution to the dynamic portfolio choice problem of an investor with power utility defined over wealth at a finite horizon who faces an investment opportunity set with time-varying risk premia, real interest rates and inflation. The variation in investment opportunities is captured by a flexible vector autoregressive parameterization, which readily accommodates a large number of assets and state variables. We find that the optimal dynamic portfolio strategy is an affine function of the vector of state variables describing investment opportunities, with coefficients that are a function of the investment horizon. We apply our method to the optimal portfolio choice problem of an investor who can choose between value and growth stock portfolios, and among these equity portfolios plus bills and bonds. For equity-only investors, the optimal mean allocation of short-horizon investors is heavily tilted away from growth stocks regardless of their risk aversion. However, the mean allocation to growth stocks increases dramatically with the investment horizon, implying that growth is less risky than value at long horizons for equity-only investors. By contrast, long-horizon conservative investors who have access to bills and bonds do not hold equities in their portfolio. These investors are concerned with interest rate risk, and empirically growth stocks are not particularly good hedges for bond returns. We also explore the welfare implications of adopting the optimal dynamic rebalancing strategy vis a vis other intuitive, but suboptimal, portfolio choice schemes and find significant welfare gains for all long-horizon investors.

Optimal Value and Growth Tilts in Long-Horizon Portfolios

We develop an analytical solution to the dynamic portfolio choice problem of an investor with power utility defined over wealth at a finite horizon, who faces a time-varying investment opportunity set, parameterized using a flexible vector autoregression. We apply this framework to study the horizon effects in the allocations of equity-only investors, who hold a mix of value and growth indices, and a more general investor, who also has access to Treasury bills and bonds. We find that the mean allocation of equity-only investors is heavily tilted towards value stocks at short-horizons, but the magnitude of this tilt declines dramatically with the investment horizon, implying that growth is less risky than value at long horizons. Investors with access to bills and bonds exhibit similar behavior, when value and growth tilts are computed relative to the total equity allocation of the portfolio. However, after accounting for the propensity of these investors to increase their total equity allocation as the horizon increases, the mean value tilt of the optimal allocation is shown to be positive and stable across time

Bayesian Inference of the Multi-Period Optimal Portfolio for an Exponential Utility

We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing Jeffreys' non-informative prior and the conjugate informative prior, we derive stochastic representations for the optimal portfolio weights at each time point of portfolio reallocation. This provides a direct access not only to the posterior distribution of the portfolio weights but also to their point estimates together with uncertainties and their asymptotic distributions. Furthermore, we present the posterior predictive distribution for the investor's wealth at each time point of the investment period in terms of a stochastic representation for the future wealth realization. This in turn makes it possible to use quantile-based risk measures or to calculate the probability of default. We apply the suggested Bayesian approach to assess the uncertainty in the multi-period optimal portfolio by considering assets from the FTSE 100 in the weeks after the British referendum to leave the European Union. The behaviour of the novel portfolio estimation method in a precarious market situation is illustrated by calculating the predictive wealth, the risk associated with the holding portfolio, and the default probability in each period.Comment: 38 pages, 5 figure

Asymmetry, Loss Aversion and Forecasting

Conditional volatility models, such as GARCH, have been used extensively in financial applications to capture predictable variation in the second moment of asset returns. However, with recent theoretical literature emphasising the loss averse nature of agents, this paper considers models which capture time variation in the second lower partial moment. Utility based evaluation is carried out on several approaches to modelling the conditional second order lower partial moment (or semi-variance), including distribution and regime based models. The findings show that when agents are loss averse, there are utility gains to be made from using models which explicitly capture this feature (rather than trying to approximate using symmetric volatility models). In general direct approaches to modelling the semi-variance are preferred to distribution based models. These results are relevant to risk management and help to link the theoretical discussion on loss aversion to emprical modellingAsymmetry, loss aversion, semi-variance, volatility models.

Long term portfolio construction

Financial analyst commonly advice individual investors with a long investment horizon to invest in portfolios comprised more of equities. This advice is usually coupled with the practice of shifting the investor's portfolio from risky asset holdings towards bonds and cash as the investor's target date gets closer. This view rests on the notion that equities tend to be less risky over the long horizon and that stock returns exhibit mean reversion overtime. The purpose of this dissertation is to find the optimal asset allocation over various investment horizons; and investigate how the optimal asset allocation changes over the long investment horizon. The study uses data from South Africa's financial market covering the period December 2001 to December 2014. The mean - variance framework generated the optimal asset allocation over 12 investment horizons. The study finds that, over 90 percent of the portfolio should be vested into fixed - income South African bonds, with little over 5 percent equities allocation, over longer investment periods. In addition, the study found evidence of time diversification on the JSE all shares index and the presence of mean reversion properties for the all s hares index. With these conclusions, implications and recommendations are suggeste

Incomplete information processing: a solution to the forward discount puzzle

The uncovered interest rate parity equation is the cornerstone of most models in international macro. However, this equation does not hold empirically since the forward discount, or interest rate differential, is negatively related to the subsequent change in the exchange rate. This forward discount puzzle implies that excess returns on foreign currency investments are predictable. In this paper we investigate to what extent incomplete information processing can explain this puzzle. We consider two types of incompleteness: infrequent and partial information processing. We calibrate a two-country general equilibrium model to the data and show that incomplete information processing can fully match the empirical evidence. It can also account for several related empirical phenomena, including that of "delayed overshooting." We show that incomplete information processing is consistent both with evidence that little capital is devoted to actively managing short-term currency positions and with a small welfare gain from active portfolio management. The gain is small because exchange rate changes are very hard to predict. The welfare gain is easily outweighed by a small cost of active portfolio management.Foreign exchange