The Portfolio Model Under RCaR Constraint

The financial market is a complex systematic engineering. With the growth of scale and complexity of financial markets, the risk of financial market also become higher, the financial crisis, originated from America, is the result of ignoring the market risk.In the field of investment, what people are most concerned is the relationship between risk and profit. Generally speaking, when enjoying higher profits, people have to bear higher risk. The investor often has the character of seeking higher expect profit and avoiding higher risk, and then get higher profit. So the investor often chose to invest in some different estate that is portfolio investment method. Portfolio investment could decrease the risk of investment, by dispersing the risk; this method could get higher profit.In the introduction part of this paper, we first introduced the necessary of analyzing portfolio investment in the current financial environment, presented the research background of this paper, reviews the development history of portfolio theory, described the research status and pointed out that the paper's main innovation points. Then, this paper described several key investment portfolio models in the portfolio area and the risk metrics CaR's definition and the Mean-CaR Model in detail. The traditional expression of CaR is based on the market parameters are constant, in this paper we analyzed and gave the CaR expression with all the market parameters changed with time.As for the shortcomings of CaR as a risk metric, that is the constraint was useless at the beginning of investment or when the wealth is less, but when the wealth is more, the constrain limit the invest too much, under the assumption of Black-Sholes Model, the Relative Capital-at-Risk constraint was introduced, which not only make the risk metrics has a more intuitive meaning, but also avoid the troubles of selecting the constraint upper bound caused by different initial wealth. Previous portfolio models often assume that the market parameters (including the return of risk assets and risk-free assets, volatility matrix) are constants, and the investment strategy is constant-rebalanced portfolio, which greatly limited the use of this model. In this paper, use RCaR as the risk metrics, a Mean-RCaR Model is established to further analyze the optimal strategy for constant rebalanced portfolio, short selling is allowed and short selling is not allowed respectively, under this model, all the market parameters were allowed to change with time. This paper gives the detail solving process of this model and then shows the explicit solution of optimal strategy. The results show that under this model, the two fund separation theorem still holds. In the end, this paper gives an example to further establish the application of this model and compare the result with the Mean-variance model, and then find some conclusion very important.