介绍

One of the factors to consider when selecting the optimal portfolio for a particular investor is the degree of risk aversion. This level of aversion to risk can be characterized by defining the investor's indifference curve. This curve consists of the family of risk/return pairs defining the trade-off between the expected return and the risk. It establishes the increment in return that a particular investor requires to make an increment in risk worthwhile. Typical risk aversion coefficients range from 2.0 through 4.0, with the higher number representing lesser tolerance to risk. The equation used to represent risk aversion in Financial Toolbox™ software is

U = E(r) - 0.005*A*sig^2

where:

U是实用值。

e（r）is the expected return.

Ais the index of investor's aversion.

sigis the standard deviation.

Optimal Risky Portfolio

该示例根据无风险利率，借贷利率和投资者的风险规避程度，计算有效边界上的最佳风险投资组合。您可以使用功能执行此操作Portalloc.

首先使用portopt.

验证= [0.1 0.2 0.15];ExpCoriance = [0.005 -0.010 0.004;-0.010 0.040 -0.002;0.004 -0.002 0.023];

考虑沿高效边界的20个不同点。

NumPorts = 20; [PortRisk, PortReturn, PortWts] = portopt(ExpReturn,...ExpCovariance, NumPorts);

Callingportopt, while specifying output arguments, returns the corresponding vectors and arrays representing the risk, return, and weights for each of the portfolios along the efficient frontier. Use these as the first three input arguments to the functionPortalloc.

Now find the optimal risky portfolio and the optimal allocation of funds between the risky portfolio and the risk-free asset, using these values for the risk-free rate, borrowing rate, and investor's degree of risk aversion.

RisklessRate = 0.08 BorrowRate = 0.12 RiskAversion = 3

CallingPortalloc不指定任何输出参数给出显示关键点的图。

Portalloc(PortRisk, PortReturn, PortWts, RisklessRate,...借贷，风险验证）；

CallingPortallocwhile specifying the output arguments returns the variance (RiskyRisk), the expected return (RiskyReturn), and the weights (风险) allocated to the optimal risky portfolio. It also returns the fraction (风险折断）分配给风险投资组合和方差的完整投资组合（整体风险）和预期的回报（OverallReturn) of the optimal overall portfolio. The overall portfolio combines investments in the risk-free asset and in the risky portfolio. The actual proportion assigned to each of these two investments is determined by the degree of risk aversion characterizing the investor.

[RiskyRisk, RiskyReturn, RiskyWts,RiskyFraction, OverallRisk,...OverallReturn] = portalloc (PortRisk, PortReturn, PortWts,...无风险，借贷，风险验证）

RiskyRisk = 0.1288 RiskyReturn = 0.1791 RiskyWts = 0.0057 0.5879 0.4064 RiskyFraction = 1.1869 OverallRisk = 0.1529 OverallReturn = 0.1902

的价值风险折断exceeds 1 (100%), implying that the risk tolerance specified allows borrowing money to invest in the risky portfolio, and that no money is invested in the risk-free asset. This borrowed capital is added to the original capital available for investment. In this example, the customer tolerates borrowing 18.69% of the original capital amount.