Abstract: The price fluctuation of risky assets brings not only the risk of investment loss, but also the opportunity of gain. Therefore, during the period of portfolio investment, every fluctuation of stock prices held by investors affects the nerves of investors, brings positive or negative utility, and impacts investors’ investment decisions. In fact, investors always look for profit opportunities from the price fluctuations of risk assets. So the price fluctuations of risk assets themselves can bring utility to investors, which is the process utility of investment. However, traditional portfolio models ignore this and only consider the utility of investment results.
   Investors can work to reduce investment uncertainty. Therefore, the process effectiveness of venture investors should be analyzed from two aspects. On the one hand, if investors grasp the ups and downs of risk assets through their own efforts, then the price fluctuation of risk assets is an opportunity for investors. Investors can timely enter and exit in the price fluctuation of risk assets, so as to make profits. Then the utility of investors is positive. The greater the volatility of asset prices there is, the greater the opportunity there is for investors to make profits, and the greater the process utility there is of their joy. On the other hand, if investors make mistakes in judgment, they will lose investment opportunities, or even suffer losses due to wrong investment. Asset price fluctuations are traps for investors, and the utility of investors is negative. The greater the price fluctuation there is, the deeper the trap there is, and the greater the dispiriting process of investors there is.
   The utility of the investor’s investment process is related to the volatility of the return rate of risk assets and the forecasting ability of the investor. If the investor correctly predicts the rise and fall of the price of risk assets, he will get the corresponding positive utility. Otherwise, if the investor makes a mistake in forecasting and fails to stop the loss in time, he will face the corresponding utility loss. The utility of investors to correctly predict the price rise of risk assets is positively correlated with the size of the price rise in risk assets. The disutility of investors to stop losses is positively related to their urgency to stop losses, and when they are closer to succeeding in stopping losses, it will be the most urgent for them to stop losses, and the disutility to stop losses will be the greatest.
   The classical prospect theory holds that people are risk averse in the face of “gain” and risk averse in the face of “loss”. However, for individual investors who use their own funds to make venture investments, they are fully responsible for the profit and loss of the investment. Due to their limited capital, energy , knowledge and experience, it is difficult for individual investors to collect enough information, and they are only followers and price takers of the risk market. All these factors make it difficult to have enough confidence to dare to take risks. Individual investors should be risk averse even in the loss stage. Therefore, this paper presents an outcome utility function representing both loss aversion and risk aversion of investors.
   This paper analyzes the influencing factors of investors’ process utility and designs the investment process utility function of venture investors. Assuming that the total utility function of investors is the linear combination of process utility function and result utility function, a portfolio model considering the process utility of investment behavior is constructed, and the solution of the model is analyzed numerically. The results show that the more the investors who are too sensitive to loss are affected by the process, the lower the proportion of funds they will invest in risk assets. The more the investors who are not sensitive to loss are affected by the process, the higher the proportion of funds they will invest in risk assets. Therefore, investors who are less sensitive to losses and more heavily affected by process utility are more likely to push up market risk. The results show that the portfolio model, which is greatly affected by the process utility of investors, performs better in the stage of continuous rise of the stock market, but worse in the stage of consolidation and continuous decline of the stock market. This shows that investors who are greatly affected by process utility will actively enter the market when the stock market continues to rise, and quickly withdraw from the market when the stock market continues to fall, thus aggravating the stock market volatility.

Key words: process utility, loss aversion, behavioral finance, investment portfolio

摘要： 传统的投资组合模型只考虑投资结果,而未考虑投资过程带来的效用影响。事实上组合投资期间投资者持有的股票价格的每一次波动都牵动着投资者的神经,带来或正或负的效用,影响投资者的投资决策。分析投资者过程效用的影响因素,设计出风险投资者的投资过程效用函数。并假设投资者的总效用函数为过程效用函数和结果效用函数的线性组合,构建考虑投资行为过程效用的投资组合模型,对模型的解进行数值模拟分析。研究结果表明:对损失过于敏感的投资者受过程影响越大,则投资风险资产的资金比例越低,对损失不敏感的投资者受过程影响越大,投资风险资产的资金比例越高。因此,对损失越不敏感且受过程效用影响越严重的投资者,越容易推高市场风险。对模型的投资绩效进行了实证检验,结果发现:受投资者过程效用影响大的投资组合模型在股市持续上涨阶段的投资表现较好,而在股市盘整阶段和持续下跌阶段表现较差。表明受过程效用影响大的投资者会在股市持续上涨时积极入市,在股市持续下跌时迅速退市,从而加剧股市震荡。

关键词: 过程效用, 损失厌恶, 行为金融, 投资组合