What Are Portfolio Loans?

The securities investment portfolio is a reasonable mix of various securities investments in order to avoid the risks of securities investment and ensure the profitability, liquidity and security of securities investments. Securities investment has many risk factors. In order to avoid the absolute risk of investing in a certain type of securities, investors generally adopt a diversified investment strategy, that is, diversify funds into several types of securities. The strength of liquidity can be reasonably matched and combined, thereby minimizing the risk of securities investment. ^[1]

Securities portfolio

Right!

The securities investment portfolio is a reasonable mix of various securities investments in order to avoid the risks of securities investment and ensure the profitability, liquidity and security of securities investments. Securities investment has many risk factors. In order to avoid the absolute risk of investing in a certain type of securities, investors generally adopt a diversified investment strategy, that is, diversify funds into several types of securities. The strength of liquidity can be reasonably matched and combined, thereby minimizing the risk of securities investment. ^[1]

Several assumptions about investor behavior

1. Investors believe that each investment option represents a probability distribution of the expected return during a certain holding period.

2. Investors seek to maximize the expected utility over a period of time, and their utility curve indicates a diminishing marginal utility of wealth.

3. Investors estimate the risk of the asset portfolio based on the variability of expected returns.

4. Investors make decisions based entirely on expected returns and risks, so that their utility curve is only a function of the expected return and the variance (or standard deviation) of the expected return.

5. At a particular level of risk, investors prefer higher returns. Similarly, at a certain expected rate of return, investors prefer less risk.

Risk Appetite and Indifference Curves

Different investors have different income preferences and aversion to risks. The existence of this difference will undoubtedly affect their choice of investment targets. Therefore, we must consider both investment risks, returns and investor preferences when looking for the optimal investment strategy.

Risk appetite

In terms of relative risk, there are three types of investors' preferences for returns: they prefer the risk type, in order to obtain higher investment returns, investors are willing to bear relatively high investment risks; and the risk-averse type, when investors obtain certain investment returns, Willing to assume relatively low investment risks; risk neutral.

Indifference curve

The investor indifference curve refers to different combinations of returns and risks that can bring the same level of satisfaction to investors. The slope of the indifference curve represents the substitution rate between risk and return. The higher the slope, the higher the return compensation that must be provided to the investor in order to take the same risk, indicating that the investor is more averse to risk. Similarly, the lower the slope, the less risk aversion the investor has.

There are many types of securities in real life, which can form countless combinations. According to Markowitz's efficient set theorem, the method of determining the optimal investment portfolio can be determined.

(1) Feasible set

A feasible set is a set of all combinations formed by n securities, and it includes all possible combinations in real life. That is, all possible combinations will be located inside or on the boundary of the feasible set. In general, the feasible set is shaped like an umbrella.

(2) Effective set

The effective set refers to the set of investment portfolios that can simultaneously meet the maximum expected return and the least risk. For a rational investor, they are risk-averse and prefer return. For the same level of risk, they will choose the combination that provides the greatest expected return; for the same expected return, they will choose the combination with the least risk. The set of portfolios that can satisfy both of these conditions is the effective set. The effective set curve has the following characteristics: The effective set is a curve that slopes to the upper right, which reflects the principle of "high return and high risk"; The effective set is an upward convex curve; The place. Click to see related graphics

(3) Optimal investment portfolio

The optimal investment portfolio is the point of indifference curve and effective set of investors. The characteristics of the effective set being convex upward and the indifference curve concave downward determine that there is only one tangency point between the effective set and the indifference curve, which means that the optimal investment portfolio is unique. For investors, the effective set exists objectively, it is determined by the securities market, while the indifference curve is subjective, and it is determined by investor risk-return preference. The higher the risk aversion, the steeper the slope of the indifference curve. The lower the risk aversion, the smaller the slope of the indifference curve.

The investor not only invests in risky assets but also invests in risk-free assets, that is to say, the portfolio of securities purchased by the investor is composed of n risky securities and 1 riskless security, or a combination of P and 1 riskless consisting of n risky securities. Securities F further allows investors to borrow money to purchase securities at a certain interest rate.

Improving the effective set using risk-free assets

Risk-free loans are equivalent to investing in risk-free assets, and the rate of return is certain. Therefore, a risk-free asset is an asset with a certain expected rate of return and zero variance. The risk-free interest rate for each period is equal to its expected value. Therefore, the covariance between the risk-free asset and any risky asset F is zero, so the risk-free asset is not related to the risky asset.

1. Investing in a risk-free asset and a risky asset

2.Investment in a risk-free asset and a portfolio

3.Improve the effective set using risk-free assets

If the investor fully invests funds in risk-free assets, the expected rate of return is RF, and the risk is zero; if the investor fully invests in the securities of the risky asset portfolio, the expected rate of return is, the risk is; investing in these two asset combinations, The expected rate of return and the size of the risk are determined by the weight WF invested in risk-free assets.

Improving the effective set using risk-free borrowing

1. Situation of risk-free borrowing and investment in a risky asset

We can consider risk-free borrowing as a negative investment, and the proportion of risky assets and risk-free borrowings in the portfolio can also be expressed as W1 and W2, and W1 + W2 = 1, W1> 1, and W2 <0. In this way, the above formula is also fully applicable to the case of risk-free borrowing. Since W1> 1 and W2 <0, it is shown on the figure as an extension line to the right of the AB line segment. This extension line greatly expands the range of the feasible set again.

2. Situation of risk-free borrowing and investment in risky asset portfolio

Similarly, the investment portfolio consisting of risk-free borrowings and risky asset portfolios has a similar relationship between expected return and risk as the investment portfolio consisting of risk-free borrowings and a risky asset portfolio.

We still assume that risky asset portfolio B is composed of risky securities and C and D, then the expected return and standard deviation of the investment portfolio consisting of risky asset portfolio B and risk-free loan A must fall on the extension line to the right of the AB line segment on.

3.Effect of risk-free borrowing on the effective set

In the case of allowing risk-free borrowing, Markowitz's effective set changes from a CTD arc to a straight line over the optimal portfolio point. When risk-free borrowing is allowed, the effective set becomes a straight line that passes through the point of the risk-free asset and is tangent to the Markowitz effective set.

4. Impact of risk-free borrowing on portfolio selection

If an investor invests to the left of the optimal portfolio point, his funds WF are invested in risk-free assets, and (1-WF) is invested in risky portfolios. This investor lends out at a risk-free interest rate, such as buying Treasury bills are actually loans to the government to collect risk-free interest. The closer you are to RF, the smaller the risk. When WF = 1, the investor invests all funds in risk-free assets; on the contrary, when WF = 0, the investor invests all funds in the risky portfolio.

If an investor invests to the right of the optimal portfolio point, WF is negative, which means that he sells (or issues) securities or borrows money from a bank at a risk-free rate or sells short to raise funds for purchasing a risky portfolio. If WF = -1, then 1-WF = 2, that is, the investor borrows funds equal to his own investable amount to invest in the risky portfolio P. The expected return on the investor's portfolio at this time is:

As borrowing increases, the expected rate of return increases linearly. Its standard deviation is:

It can be seen that when borrowing increases, the risks will increase.

Conclusion: The interest-free risk loan is on the left of the optimal portfolio point, and the risk-free loan is on the right of the optimal portfolio point.