Portfolio Management

In this lesson, you’re expected to learn about:
– the relationship between risk and returns
– finding the best risk/return balance
– measuring and optimizing risk

Risk Aversion

The risks that you can eliminate or greatly minimize through diversification are specific risks – those associated with an individual investment.

Specific risks include default risk on a bond, liquidity risk on the company underlying a share and the risk of a building losing value in the property market.

Systematic Risk 

However this strategy can’t stop the entire economy as a whole from being affected. Sometimes, no matter how perfect an individual asset is or how well a portfolio is diversified, a nation’s economy essentially collapses and everything loses value.

To minimize systematic risk, your options are to diversify internationally – national economies tend to change at different rates just like individual investments.

Risk-Free Investments

What are risk-free investments?
Short-term, fixed-rate, highly liquid assets (such as bonds) issued by organizations with great credit scores are considered to be risk-free.

Treasury Bills

Treausry Bills are a good example of risk-free investments. The amount of risk associated with treasury bills is so small that they’re considered risk-free.

– mature in as little as a few weeks
– issued by the government
– have a fixed return
– can be easily sold

However, the problem is that they also offer very low returns.

Measuring Risk Aversion 

Often the amount of risk aversion that a company has depends on its timeline.

Portfolios with short-term goals are usually more risk averse because they have less time to make up for any losses.

Long-term portfolios can ride out any losses from systematic risk by waiting for the economy to regain strength.

Aversion Function 

A number of methods can be employed to measure how risk averse a particular business or investor is. Many financial advisors measure risk aversion in terms that don’t use a risk function and instead choose to use only their time horizon.

Modern portfolio theory uses something called an aversion function. This function is measured by determining how much additional return a company must think is possible to be willing to take on just one additional unit of risk. Risk is measured as the probability of loss (p), while (1 – p) is the probability that no loss will be experienced.

Thus, the aversion function measures how much additional return must be generated for a single unit of additional risk.

The function changes depending on how much risk the company has already incurred but is measured by dividing the percentage change in expected returns required by the company by a percentage change in risk.

Approaches to Measuring Risk

In this lesson, we’ll look at two primary approaches to measuring risk:
– Capital Asset Pricing Model (CAPM)
– Arbitrage Pricing Theory (APT)

Today the CAPM is seen as an unrealistic view of investing but it’s still valid as a starting point upon which to build better and more practical models.

The CAPM leads to the use of arbitrage pricing theory (ACT), which is more flexible and has gained more credibility as a functional approach to quantifying portfolio management.

In both cases, the goal is to assess whether an investment is worth pursuing by determining the rate of returns and the risk compared to the risk-free rate of returns.

1) Capital Asset Pricing Model (CAPM)

Let’s start by looking at the CAPM equation:

Understanding the CAPM Equation

By subtracting the risk-free rate from the market rate of return, you’re determining what market premium is being offered for investing in risky assets.

Investors want a return premium that’s higher than the risk-free rate so you add the risk-free rate back into the equation to get the rate of returns demanded by investors to entice them to purchase an investment under CAPM.

Beta (ß), i.e. the level of risk on a specific asset, is actually a measure of volatility, which means that a particular investment can fluctuate far above normal market returns and still be considered high-risk, even though it’s making huge gains compared to the market.
Measures of risk used by value investors (investors who focus on finding undervalued and overvalued assets) use primary measures that compare accounting values to market prices.

The exact methods used to determine risk vary from investor to investor. Investors don’t like to talk about their methods in case they give away a ‘trade secret’.

CAPM is imperfect because to be functionally useful it requires several assumptions of perfect data. 

No one has a perfect market portfolio or perfect access to information. CAPM ignores factors of behavioral finance and it assumes that all returns above market returns will be lost in the long run and that the distribution of returns in a market portfolio is statistically perfect.

2) Arbitrage Pricing Theory (APT)

APT is far more flexible and effective than CAPM.

Instead of worrying about returns on a market portfolio, APT looks for differentials in the market price of a single investment and what the market price of the same investment actually should be.

You can think of it in terms of volatility measures. The expected returns on an investment change in response to other factors and the sensitivity that the investment has to that factor.

When the price of an investment is lower than the price predicted by the model, you should purchase it because the prediction is that it’s undervalued and is going to generate more value or increase in value in the future.

If a price is higher than the price predicted by the model, the investment is considered overvalued and you should sell it.

The APT Model

Let’s now see what the APT equation looks like.

Understanding the APT Equation

In APT, beta (ß) measures something similar to CAPM – the amount of change in returns caused in response to a change of a particular variable. That variable can be interest rates, GDP, annual sales or anything else that influences the returns on an investment.

The APT model doesn’t really take risk into consideration because it’s not using measures of probability to determine the value of the investment. Instead it’s looking for differentials in value of the current market price and the price that the investment should have. Therefore, the only risk to be concerned with is market risk – the state of being over- or undervalued has already been established rather than relying on probabilities of risk.

The variable e is meant to account for short-term variations in the value of an investment caused by unrelated or temporary influences.

Overall, APT isn’t very different from CAPM. They both rely on changes in value in response to a specific variable, both use the beta function and both expect returns over the risk-free rate.

Optimizing portfolio risk
Collections of individual assets interact together to influence the overall portfolio.

So when several investments are lumped together in a portfolio, every single investment has an influence on the portfolio.

The Efficient Frontier 

An efficient frontier is the maximum amount of returns that can be generated for a given level of risk in a portfolio.

In the figure below, the straight line labeled ‘Best possible CAL’ * illustrates the best potential proportion of returns on risk.

* CAL stands for capital allocation line, which means that any optimized portfolio falls on that line.
However, individual assets don’t fall on that line and so you have to use diversification of your portfolio to make that happen. Because investments that change value in opposite directions reduce risk below the risk of any individual asset through diversification, you can decrease the total risk of a portfolio, shifting it to the left, at any given rate of return.

The portfolio is optimized at the point of tangency, where the efficient frontier intersects the best possible CAL using a given investment portfolio. The point where the lines intersect in the figure shows the point of an optimized portfolio generated using the individual investments illustrated by the other dots.

[Optional] Efficient Frontier
To ensure that you’re maximizing the opportunity of getting the highest expected return for a given level of risk, and to measure the influences that individual investments have on the risk and return on the whole portfolio, you need to use an equation.

According to CAPM, you measure the returns on a portfolio using the equation below.

This equation says that the returns on a portfolio are the sum of the returns of the individual investments weighted by the proportion of their contribution to the portfolio.

Above-normal returns

A big part of professional portfolio management that allows some investors to generate returns over and above usual returns comes from technology.

Another observation about these above-normal returns in a portfolio is that many of the successful portfolios lose their gains during an economic downturn, such as a recession.

Mitigating Risk 

You can mitigate this drawback by carefully watching the national economy and taking the following precautions when indicators start pointing towards a downturn:

– start buying options
– start selling some of your portfolio
– transition to lower-risk investments
– continue to take risk by short-selling assets


New innovations for portfolio management emerge all the time – new calculations, new models, new advances in mathematics and statistics, and new technologies.

Plus, new and better ways to measure risk, find combinations of factors that influence APT calculations and identify more accessible markets arise as well.

[Optional] Portfolio Management
Jim Rohn Sứ mệnh khởi nghiệp