This is fourth post in the series *how to get into portfolio management*. In this post, we will cover the basics of Financial Portfolio Management – what is CAPM, Beta, Market Risk Premium and Risk Free Rate. We will also see how to calculate beta of any stock.

**Diversification and Beta**** **

We diversify the portfolio to reduce total risk. By doing this, only systematic risk remains. Beta is used to measure systematic risks. A conservative investor would look for beta of 0.5 whereas an aggressive trader would look for the betas around 1.5. If one is looking for reducing total risk, he should go for good diversification strategy instead of lower betas.

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**Capital Asset Pricing Model**** **

In finance, the Capital Asset Pricing Model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset’s non-diversifiable risk. The model takes into account the asset’s sensitivity to non-diversifiable risk (also known as systemic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

The model was introduced by **Jack Treynor, William Sharpe, John Lintner** and **Jan Mossin** independently, building on the earlier work of **Harry Markowitz** on diversification and modern portfolio theory. Sharpe received the Nobel Memorial Prize in Economics (jointly with Markowitz and Merton Miller) for this contribution to the field of financial economics.

The CAPM is a model for pricing an individual security or a portfolio. For individual securities, we made use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio.** **

The Capital Asset Pricing Model (CAPM) represents the relationship between the expected risk and expected return.

**Assumptions of CAPM**

All Investors:

1) Aim to maximize utilities.

2) Are rational risk-averse.

3) Are price takers i.e. they can not influence prices.

4) Can lend and borrow unlimited under the risk free rate of interest.

5) Securities are all highly divisible into small parcels.

6) No transaction or taxation costs incurred.

Application of CAPM requires following inputs:

1. Risk-free rate

2. Market Risk Premium

3. Beta

**Risk-free rate**

The risk-free rate is the return on a security or even a portfolio of securities which is void of default risk and is not interrelated to returns from anything else in the economy. In theory, the best estimate of the risk-free rate is the return on a zero-beta portfolio. However, constructing zero beta portfolios is an expensive and complex affair and hence they are mostly unavailable for risk-free rate estimation.

Two alternatives are most commonly used in practice:

1. The rate on a short-term government security like the 364-days Treasury bill.

2. The rate on a long-term government bond with maturity of 15 to 20 years.

** **Each of the above alternatives has its own pros and cons and the choice depends extensively on the judgment of the analyst.

**Market Risk Premium**

The risk premium in CAPM is usually based on historical data and it’s computed as the difference between the average return on stocks and average risk-free rate. In this context, two measurement issues need to be tackled: What should be the duration of the measurement period? Should geometric mean or arithmetic mean be used?

The answer to the first question is to use the longest possible historical period, lacking any risk premium trends over the course of time.

Practitioners appear to disagree over the option of geometric versus arithmetic mean. The geometric mean is the compounded annual return over the period of measurement where as arithmetic mean is the average of annual rates of return over the measurement period.

**Determinants of Risk Premium**** **

The market risk premium is primarily influenced by three factors:

**Discrepancy in Underlying Economy:**

Risk premium is likely to be large if the underlying economy is more volatile. For instance, the risk premiums for budding markets, taking into account their high-growth rate and high-risk economies, are larger than that for developed markets.

**Political Risk:**

Risk premiums are often more in markets that are exposed to higher political volatility. It should be noted that political instability causes uncertainty in an economy.

**Market Structure:**

Risk premium is smaller if the companies listed on the market are large, steady and diversified. Whereas, for small companies listed on the market, risk premium is larger.

3. **Beta**

Beta is a relative measure of risk associated with the company’s shares as against the market as a whole. Beta measures the volatility of the stock. When the market is going up, the stocks which have higher betas (more than 1) are preferred and in falling markets the stocks having lower betas (less than 1) are preferred.** **

**Calculation of Beta**** **

The calculation of beta may be illustrated with an example. The rates of return on stock A and the market portfolio for 15 periods are given below:

Period | Return on stock A (RA | Return on market portfolio, RM | Deviation of return on stock A from its mean (RA – mean of RA) | Deviation of return on Market Portfolio from its mean (RM – mean of RM) | Product of the deviation, (RA – mean of RA) (RM – mean of RM) | Square of the deviation of return on market portfolio from its mean (RM – mean of RM)2 |

1 | 10 | 12 | 0 | 3 | 0 | 9 |

2 | 15 | 14 | 5 | 5 | 25 | 25 |

3 | 18 | 13 | 8 | 4 | 32 | 16 |

4 | 14 | 10 | 4 | 1 | 4 | 1 |

5 | 16 | 9 | 6 | 0 | 0 | 0 |

6 | 16 | 13 | 6 | 4 | 24 | 16 |

7 | 18 | 14 | 8 | 5 | 40 | 25 |

8 | 4 | 7 | -6 | -2 | 12 | 4 |

9 | -9 | 1 | -19 | -8 | 152 | 64 |

10 | 14 | 12 | 4 | 3 | 12 | 9 |

11 | 15 | -11 | 5 | -20 | -100 | 400 |

12 | 14 | 16 | 4 | 7 | 28 | 49 |

13 | 6 | 8 | -4 | -1 | 4 | 1 |

14 | 7 | 7 | -3 | -2 | 6 | 4 |

15 | -8 | 10 | -18 | 1 | -18 | 1 |

Table : Calculation of Beta

These are important factors in **portfolio management/Stock Portfolio Management**.

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