Downside Risk Control in Continuous Time Portfolio Management

• Published date: 01 December 2013
• Author: Shih‐Chieh Bill Chang,Han‐Cong Cai,Ya‐Wen Hwang
• DOI: http://doi.org/10.1111/ajfs.12035
• Date: 01 December 2013

Downside Risk Control in Continuous Time

Portfolio Management

Ya-Wen Hwang*

Department of Risk Management and Insurance, Feng Chia University

Shih-Chieh Bill Chang

Department of Risk Management and Insurance, National Chengchi University

Han-Cong Cai

Nan Shan Life Insurance Company, Ltd

Received 8 February 2013; Accepted 25 July 2013

Abstract

Institutionally managed savings have dramatically increased in recent decades. In order to

ensure that portfolio managers work directly for investors, controlling downside risk is a cru-

cial mechanism in the agent’s asset allocation strategy. In this paper, we extend the agent’s

asset allocation problem by incorporating multi-period downside control over the time-vary-

ing opportunity set. We show that optimal asset allocation can be regarded as a series of sep-

arate dynamic strategies in replicating the synthetic call options with the utility-related

mutual fund and guarantee exercise. Numerical simulations show that increasing the mini-

mum effectively increases the equity holding. Moreover, fund managers are inclined to hold

only fixed income portfolios once the target return is obtained.

Keywords Multi-period downside control; Dynamic strategies; Synthetic call; Mutual fund

JEL Classification: C61,D81,G11

1. Introduction

Recent decades have witnessed a dramatic increase in institutionally managed sav-

ings, both in absolute terms and relative to household financial wealth (Davis and

Steil, 2001; Bank for International Settlements (BIS), 2003). Moreover, asset man-

agement of pension funds also tends to be delegated to a third party to increase

potential investment efficiency. For example, more than 50% of the Labor Pension

Fund’s assets in Taiwan are delegated to portfolio managers.

*Corresponding author: Ya-Wen Hwang, Department of Risk Management and

Insurance, Feng Chia University, 100 Wenhwa Road, Seatwen, Taichung 40724, Taiwan.

Tel: +886-4-24517250 ext 4108, Fax: +886-4-24512176, email: ywhwang@fcu.edu.tw.

Asia-Pacific Journal of Financial Studies (2014) 42, 913–938 doi:10.1111/ajfs.12035

©2013 Korean Securities Association 913

It is important to ensure that portfolio managers work directly for investors. A

number of studies examine potential moral hazards and information asymmetry prob-

lems that can arise between investors and portfolio managers (see, e.g. Brown et al.,

1996; Chevalier and Ellison, 1997; Ou-Yang, 2003; Chen and Pennacchi, 2009). Most

investment contracts between settlers and trustees include certain downside protecti on

mechanisms, the simplest of which is to set the benchmark. Basak (1995) examines the

effects of portfolio insurance on market and asset price dynamics in a general equilib -

rium continuous-time model. Grossman and Zhou (1996) examine Merton’s (1971)

classical portfolio optimization problem of under the drawdown constraint.

However, the shortcomings of downside protection of the benchmark are that it

is costly and limits potential upside performance investment strategy. Researchers

provide tracking error constraints, which means that not delivering a target return

(benchmark return) is allowed with a pre-specified shortfall probability. Roll (1992)

investigates the investment strategy under minimizing the tracking error variance

for a given expected tracking error. Basak and Shapiro (2001) compare the perfor-

mance of VaR risk management and limited expected losses risk management. Ba-

sak et al. (2006) demonstrate that losses of the investment portfolio under tracking

error constraints can be further reduced relative to those under downside hedging

in the constant interest rate environment.

On the other hand, consideration of the incentive and moral hazard problems

of an agent’s asset management can be found in Ou-Yang (2003), Basak et al.

(2007), and Ju and Wan (2012). In this paper, we focus on the influence of the

optimal agent’s asset allocation strategy by the downside protection strategy; thus,

incentive and moral hazard are not incorporated in this study.

The above studies focus on discussing the downside protection of terminal wealth.

In reality, however, settlers could monitor performance at any point during the con-

tract. For example, the newly revised investment mandate from the Bureau of Labor

Insurance in Taiwan states that when a fund managed by a trustee (investment man -

ager) depreciates more than 10% of the initial fund wealth, 15% of the delegated asset

must be returned to the settler (original investor). When the managed fund depreci-

ates more than 14% of the initial fund wealth, the total managed asset must be

returned to the settler. In the meantime, the settler can monitor the performance of

the fund investment twice a year. If the investment performance does not satisfy mini-

mal requirements, the Bureau of Labor Insurance can terminate the investment con-

tract. Therefore, in this paper, we extend the agent’s asset allocation problem by

incorporating multi-period downside control over the time-varying opportunity set.

1

1

Papers incorporating stochastic interest rate models can be found in Bajeux-Besnainou and

Portait (1998), Sorensen (1999), Brennan et al. (1997), Barberis (2000), Deelstra et al. (2000),

Campbell and Viceira (2001), Omberg (2001), Wachter (2003), Bajeux-Besnainou et al.

(2003), Munk and Sorensen (2004), Sangvinatsos and Wachter (2005), Liu (2007) and others.

These papers demonstrate that the optimal investment strategy is influenced by the volatility

of interest rates.

Y.-W. Hwang et al.

914 ©2013 Korean Securities Association