# Overview on Portfolio Management

Updated: Nov 12

Portfolio management is a useful strategy for business objectives. Below, the different phases of portfolio management are elaborated on. However, the focus lies on asset allocation. An in-depth explanation of the Modern Portfolio Theory is provided.

**Planning step**

**Active VS passive investors**

There are two types of investment styles:

· ** Passive investors**

Passive investors follow the **efficient market hypothesis**. So, share prices reflect all available information. Therefore, they believe that in the long run, it’s impossible to beat the market.

· **Active investors**

Active investors are more related to **portfolio management**. They believe they can outperform the market by selecting an **optimal portfolio**. However, to be profitable, the return needs to be high enough to **cover all costs** involved.

**The Investment policy statement**

For portfolio planning, strategies should be studied to construct a proper portfolio. The **investor policy statement **is a written document drafted by portfolio managers. It outlines and understands the investors’ features and expectations. Therefore, it contains:

- The overall investment **objective**;

- The **return, distribution, and risk requirements**;

- **Risk tolerance** of the investor

- **Relative constraints**

- **Other considerations** relevant to the investment strategy

**Risk aversion**

Risk aversion is the tendency to prefer low-uncertainty settings over high-uncertainty ones:

· **Very risk-averse **investors choose to **safeguard the liquidity** of their investments. Due to this, their portfolios do not contain volatile assets. Examples are government bonds, certificates of deposits, and treasury securities.

· ** Risk-neutral** investors do not take risk into account. So, their decision is based only on **potential gains**.

· **Less-risk-averse** investors are willing to take on **more risk **for higher rewards.

**Execution step**

The chapter begins with a brief overview of some elements essential to understand portfolio theory.

**Standard deviation as measure of risk**

Standard deviation is a measure of how much an investment's returns can vary from its average return. The average return can be computed:

· arithmetically as the **mean return:**

· geometrically using the formula of the **holding period return**:

**Standard deviation** measures the dispersion of data concerning the average return. A high value deviates from the average, meaning increased uncertainty and risk.

According to the figure, there is a 99,73% probability of the return falling in the range. So, a lower standard deviation decreases the range and **lowers uncertainty **and the possibility of loss.

**Diversification**

Diversification is a way to **reduce the risk** of a portfolio. The core idea is that assets move in **different directions**. Therefore, getting similar assets increases risk. Instead, with different assets, a bad performance will be made up for by another asset.

**Covariance and correlation**

The indicator used to express this concept is **covariance**. It measures the relationship between two random variables. Also, it evaluates to what extent the variables change together:

**Positive**covariance: Indicates that two variables tend to move in the**same direction****Negative**covariance: Indicates that two variables tend to move in**inverse directions**

The following formula determines the **degree of strength **in the relationship:

in case of correlation being less than 1, diversification can reduce the risk of the portfolio. At 1, the risk of a portfolio with two assets is similar to the sum of the risk of holding separate assets. In all other cases, a portfolio is less risky as returns and losses offset each other.

**The Markowitz model **

The Markowitz model is a **portfolio optimization model**. It holds the idea that a rational investor:

· When given two portfolios with equal risk, would prefer the one with higher return.

· When given two portfolios with equal return, would prefer the one with lower risk.

So, instead of choosing between these two options, we can **combine** both and seek to **minimize** this equation:

· "x" is the proportion of money invested in each asset, where the sum of all x is 1.

· "Lambda" is the risk-return preference level.

The aim is to solve **optimum x*** vector through various values of lambda. Then, the **expected return** and **standard deviation** values can be computed. Afterward, the true **efficient frontier** can be drawn to suggest the most efficient portfolio.

**The Modern Portfolio Theory **

According to this theory, investors should select a portfolio from the efficient set, depending on their risk appetite. MPT lies in two strong assumptions. Firstly, **markets are efficient**. Secondly, the **correlation** **between assets is fixed**, whereas it is not constant in the real world.

**Asset allocation**

Asset allocation deals with finding the proper** combination** between the risky portfolio and the **risk-free assets**. When adding a risk-free asset to the risky portfolio, the risk is reduced. This is because the low volatility reduces the variance of the portfolio. Investors can decide the risk and risk-free proportion by moving along the **Capital allocation line**. In general, the portfolio that respects the tangency condition with one of the capital allocation lines is the **optimal risky portfolio**. The line is called the **Capital market line.**

**Security selection**
This part of the selection of stock **forms the portfolio**. A **fundamental analysis** is made of the **security sector**. Indicators such as price-earnings, price-book, price-cash flow, and revenue and earnings growth are used. These can be found in the **Exchange Traded Fund** (ETF). Furthermore, it’s important to **evaluate the risk** carried by each security. This contributes to the risk of the portfolio. Also, it can be evaluated if it is **systematic or unsystematic**.

**Idiosyncratic/unsystematic risk**
This is the risk specific to each asset. It’s a **company-specific** risk and depends on factors like new competitors or the launching of new products. Unsystematic risk is foreseeable and can be offset by **diversification**.

**Systematic risk **

Risk common for the **entire market**. The cause factors are beyond the control of the company or individual. So, it is **external** to the organization. Since all assets carry the risk, it is **non-diversifiable**. There are four types:

· **Market risk**: the tendency of investors to follow the direction of the market.

· **Interest rate risk**: changes in the price of a security due to changes in interest rate

· **Purchasing power risk**: in case of positive inflation, a lack of proportional income growth decreases purchasing power.

· **Exchange rate risk**: uncertainty associated with changes in the value of foreign currencies

Using diversification investors can reduce the idiosyncratic risk, but not the systematic risk. Therefore, there is a **minimum amount of risk** that all investors have to bear, intrinsic in the market.

**Beta as a measure of systematic risk**

Beta is the indicator of systematic risk. It measures the movement of an asset according to the movement of the **overall market portfolio.** Thus, it is an** indicator of volatility**. The beta represents the **contribution of stock** to the non-diversifiable risk to the market portfolio.

**The Capital Asset Pricing Model **

Investors are willing to take on more risk than the risk-free rate only if they receive a higher level of return. This is called the **risk premium**. The CAPM formula allows investors to calculate the expected return per risk. Therefore, the Capital Asset Pricing Model describes the relationship between **systematic risk** and **expected return**. The latter discounts the expected dividends and capital appreciation of the stock over the expected period.

· The risk-free rate: the time value of money.

· The beta

· The factor is the market risk premium. This is the additional return an investor will receive from holding a risky market portfolio.

The **security market line **is the graphical representation of the CAPM model. It is an upward-sloping curve, with **β** as slope and the **risk-free rate** as intercept. This is the minimum return an investor can obtain, corresponding to 0 risk level.

**Evaluating step **

**Re-balancing**

When re-balancing, the allocation of assets in the portfolio is adjusted to the **investor’s preference**. The value of assets changes over time. Therefore, investors need to **regularly re-balance** the weights of their investments. Thus, they maintain the desired proportion between risky and risk-free assets. There are two classes of re-balancing:

· **Constant mix strategy**: the weight of the holdings does not change

1. **Calendar re-balancing:** adjusting to the original allocation at a desired frequency.

2. **Percentage of portfolio re-balancing:** every asset has a target and range for its value. The portfolio is re-balanced when an asset jumps outside the range.

**Constant proportion portfolio insurance**: The assumption that as the value of the portfolio increases, risk tolerance becomes higher. Consequently, a higher percentage will be invested in risky assets.

## Conclusion

Portfolio management is the building of an optimal portfolio for each active investor. Firstly, targeted risk, risk tolerance, and constrains are determined through the **Investment Policy Statement.** Secondly, the **efficient frontier** is found through the **portfolio theory**. Then, **asset allocation** is applied. Fourthly, the portfolio manager proceeds with **stock selection**. However, after building the portfolio, regular modification is still needed. Therefore, **re-balancing** is an intrinsic part of the process.

**Sources**

Active_Portfolio_Management-with-cover-page-v2.pdf (d1wqtxts1xzle7.cloudfront.net)

DARWIN Filters: A Practical Alternative to Markowitz Portfolio Theory | Darwinex Blog

Modern Portfolio Theory (MPT) - Overview, Diversification (corporatefinanceinstitute.com)

Systemic Risk - Understanding How Systemic Risk Affects the Economy (corporatefinanceinstitute.com)

Beta Definition: Meaning, Formula, & Calculation (investopedia.com)