Introduction

principal-agency relationships in the current economy. The mandates in the contract become an important factor in reducing the principal-agent problem in a delegated portfolio management framework.

Pension funds are predominantly managed by corporate treasures, who often delegate the asset management to a third party, thus creating an additional layer of agency. In order to reduce the principal-agent cost in delegated fund management, some targets for the fund managers are included into the investment contract between settlers and trustees. According to the newly revised investment mandate of the delegated portfolio management from the Bureau of Labor Insurance in Taiwan, when the fund managed by the trustee (investment manager) depreciates more than 10 percent of the initial fund level, fifty percent of the delegated asset will be return to the settler (original investor). When the managed fund depreciates more than fourteen percent of the initial fund level, the total managed asset will be return to the settler. In the meantime, the performance of the fund investment is monitored by the settler

‧

twice a year. If the investment performance is not satisfying the minimal requirements, the Bureau of Labor Insurance can terminate the investment contract. Hence the delegated fund manager will be facing the investment dilemma between having the upside gain in the bull market and providing the downside protection in the bear market, i.e. the floor protection mandate when the more aggressive strategy is employed and the minimal annual 7% return on return requirement when the more conservative investment strategy is employed.

In order to achieve the investment mandate of the investors, how to effectively and efficiently determine the asset allocation in the delegated fund management has become a crucial issue. Asset allocation is a dynamic process of choosing various assets in the investment portfolio. Asset allocation made by the fund manager is heavily influenced by the design of contract between trustee and the fund managers.

The result of asset allocation varies due to the risk profile and risk attitude of the fund manager and the mandate given by the investors. Hence, asset allocation is a decision making process to invest amount of the assets and the asset classes which meet the demands and objectives through some given mandates.

Traditionally, the delegated fund is allocated among various assets or asset classes. The asset weights are fixed ratios employing the tactic asset allocation which are influenced by the risk tolerance of the investors, market information, and the

‧

expected objective determined preliminarily. Although this approach reduces risk by diversification, it does not concern the situation of the market immediately. Because the diversification theory suggests that several assets in the portfolio will be appreciated while others will be depreciated, then the positive effects will be offset the negative impacts when the portfolio is full diversified. However, if the market is in the recession period, then the tactic allocation approach will not fully employ the market information. In other words, the allocation decision will not change significantly even facing a great loss, and the return from the assets sometimes lags behind the performance of the delegated portfolio. Hence diversification strategy could result in poor performance and sometimes far away from the benchmark.

Dynamic asset allocation which is similar to the tactic asset allocation in reducing risk through diversification among different assets or asset classes, but it also adjust the weights within various asset categories based on updated market information in order to seek potential opportunities to have superior returns. One of the benefits of dynamic asset allocation is to eliminate risks without scarifying returns.

To protect the downside risk of a portfolio is not so difficult. All one has to do is to raise the weights of low risk assets like Treasury Bills. However, lowering the risks of the portfolio also results in lower returns. Besides that, we can find financial market tends to move in cycles. It is not wise to employ tactic asset allocation when the

‧

Effective and efficient downside control approaches are especially important for the delegated fund managers to deal with certain long-term funds which include insurance funds, pension funds, or endowment funds, etc. In order to control these downside risks and maximize the projected investment yield, we assume that the objective of the delegated fund managers is to maximize the expected utility of wealth of the long-term fund at the end of each period. Furthermore, we also ask the fund managers that the wealth of the delegated fund at the end of each period must at least be equal to the criterions which have been promised at the beginning or even be higher than them. In this study, we employ the dynamic fund separation theorems (Merton, 1971) to construct the optimal dynamic asset allocation of the delegated portfolio. Then, we can derive that the optimal asset allocation strategy is just equivalent to hold risk free asset and hedging portfolio with a European option which can be replicated by the market primary assets.

The rest of this paper is organized as follows. Section 2 reviews some of the papers, and introduces the tool we used and the history of development of optimal asset allocation. Section 3 describes the models we have developed. They include the

‧ 國

立 政 治 大 學

‧

N a tio na

l C h engchi U ni ve rs it y

5/66

models for financial markets which is like Vasicek’s interest rate model and Geometric Brownian Motion models for stocks and models for hedging portfolio which is derived from using martingale techniques, starting from the basic framework and followed by the dynamics of invested assets and downside constrains. Section 4 presents the numerical results through some examples. Moreover, we will try to explain how fund managers do asset allocation and discuss if there are some relationships between the choices of mandates and the behavior of fund managers.

Most important of all, we will consider if separating the delegated fund into multi-period is needed and the selection of constrains will how to influence fund managers to do asset allocation. Conclusions are made in Section 5.

‧