# Mastering Advanced Portfolio Concepts

## The Uniform Investment Adviser Law Examination

#### Alpha

A stock’s alpha is its projected independent rate of change or the difference between an investment’s expected return and its actual return. Portfolio managers whose portfolios have positive alphas are adding value and increasing the return through their asset selection.

#### Beta

A stock’s beta is its projected rate of change relative to the market as a whole. If the market was up 10% for the year, a stock with a beta of 1.5 could reasonably be expected to be up 15%. A stock with a beta greater than one has a higher level of volatility than the market as a whole and is considered to be more risky than the overall market. A stock with a beta of less than one is less volatile than prices in the overall market and is considered to be less risky. An example of a low beta stock would be a utility stock. The price of utility stocks does not tend to move dramatically. A security’s beta measures its non-diversifiable or systematic risk. For each incremental unit of risk an investor takes on, they must be compensated with additional expected returns. If the portfolio’s actual return exceeds that of its expected return, the portfolio has generated excess returns. The Sharpe Ratio can measure a portfolio’s risk adjusted return. If two portfolios both return 8%, but portfolio A contains dramatically more risk than portfolio B, then portfolio B is a much better investment choice. The Shape Ratio will tell an investor how well they are being compensated for the investment risk they are assuming. The Shape Ratio takes the portfolio’s return and subtracts the “risk free return” offered on short-term Treasury bills (usually 90 days) to determine the level of return that the investor earned over the risk free return. The risk premium is then divided by the portfolio’s standard deviation. The Sharpe Ratio appears as follows:

Sharpe Ratio = |
(R- RFR)SD |

Series 65 candidates will have to be able to identify The Shape Ratio, but most likely will not be required to calculate it.

#### Expected Return

Modern portfolio managers try to manage risk and evaluate investments by employing a variety of concepts under modern portfolio theory. Modern portfolio theory states that the expected rate of return for an investment is the sum of its weighted returns. An investment’s weighted return is its possible return multiplied by the likelihood of that return being realized. The following table details the expected return for XYZ:

Opinion |
Expected Return |
Probability ofExpected Return |
Weighted Return |

Outperform |
20% |
25% |
5% |

Market perform |
10% |
50% |
5% |

Underperform |
5% |
25% |
1.25% |

Expected Return |
11.25% |

The following table details the expected return for ABC:

Opinion |
Expected Return |
Probability ofExpected Return |
Weighted Return |

Outperform |
40% |
10% |
4% |

Market perform |
20% |
70% |
14% |

Underperform |
(33.75%) |
20% |
(6.75%) |

Expected Return |
11.25% |

Notice that the expected rate of return for both XYZ and ABC is 11.25%. However, an investment in XYZ contains less risk than an investment in ABC because the distribution of potential returns is not as wide as the distribution of potential returns for ABC. An investor who is considering investing in either XYZ or ABC would consider the 11.25% expected return offered by XYZ to be more attractive than the same expected return offered by ABC. The distribution of an investment’s varying expected returns is measured by the investment’s standard deviation. The wider the distribution of an investment’s expected returns, the greater its standard deviation. Investments with higher standard deviations contain more risk than investments with lower standard deviations. As an investment’s results are plotted over time, there is a 95% chance that its actual return will be within two standard deviations of its expected return and a 67% chance that it will be within one standard deviation of its expected return. Portfolio managers will use computer simulations to examine the possibilities of various portfolio strategies. The Monte Carlo simulation is one such simulation used by portfolio managers.

#### Time Value of Money

As time progresses, inflation eats away at the value or the purchasing power of the dollar. That is to say that a dollar today is worth more than a dollar tomorrow. Investors can determine the future value of a sum invested if they know the interest rate, the time horizon, and the compounding schedule. The future value of a sum invested today can be determined by using the following formula:

**FV = PV (1 + R) ^{T}**

**FV = Future Value PV = Present Value R = Interest rate
T = The number of compounding periods for which the money will be invested**

Example:

FV = ?

PV = $1,000

R = 5%

T = 5 years compounded annually

**FV = $1,000 (1 + .05) ^{5}
FV = $1,000 (1.276)**

FV = $1,276

The future value of the investment will increase as the number of compounding periods increases. Let’s look at what would happen to the same investment of $1,000 for five years at 5% if the interest was compounded semiannually. Everything would remain the same except T would be 10 and the interest rate for each semi-annual period would be half the annual rate. In this example we get:

**FV = $1,000 (1 + .025) ^{10}
FV = $1,000 (1.28)**

FV = $1,280

More compounding periods increase the investor’s total return.

An investor can also determine the present value a future payment by using the following formula:

PV = |
FV(1 + R) ^{T} |

An investor can also use the present value formula to determine how much they would have to invest today to have a given sum of money in the future. For example, let’s say that an investor wants to have $10,000 saved for their child’s college tuition five years from now. If the investor knows that they can receive 6% on their money, they can determine how much they must invest today. The present value of $10,000 five years from now at a 6% rate is found as follows:

PV = |
$10,000(1 + .06) ^{5} |

PV = |
$10,0001.338 |

PV = |
$7,473 |

The investor would have to invest $7,473 today at a 6% rate to have $10,000 five years from now. Investors can also use the present value and future value to determine an investment’s internal rate of return through a process call iteration. Series 65 candidates will not have to calculate an investment’s internal rate of return.

#### Modern Portfolio Theory

As money management developed over the last century, analysts began to shift their focus from the returns available from individual investments to the returns available from an entire portfolio. This approach became known as modern portfolio theory. Modern portfolio theory is based on the concept that investors are risk adverse. Through diversification of investments and asset classes, portfolios can be constructed with higher levels of expected return for each unit of risk assumed. Asset classes are divided into three main categories, stocks, bonds, and, cash and cash equivalents. Portfolio managers, through modern portfolio theory, can construct portfolios based on various allocations over the three main asset classes whose return will be the greatest given each unit of risk. This level of optimal performance is known as the efficient frontier. Any portfolio whose returns are expected to be less than optimal are said to be operating behind the efficient frontier. Optimal portfolio performance will be achieved by constructing a portfolio whose securities prices move independently of one another or whose prices move inversely to one another. Allocating a client’s assets over various asset classes to achieve a given investment objective is known as strategic asset allocation. As the investment results of the different asset classes vary over time, the assets may have to be rebalanced. Asset rebalancing can be divided into two categories: systematic rebalancing and active rebalancing. Systematic rebalancing is designed to keep the original asset allocation model in place. For example, if a client’s portfolio is designed to be 70%/25%/5% in stocks, bonds, and cash respectively, as the percentages shift, the portfolio manager would rebalance the assets to maintain the original percentages. Systematic rebalancing can be done at regular intervals such as quarterly or whenever the asset allocation shifts by a certain percentage, such as by five percent or more. Active rebalancing assumes that a portfolio manager can effectively shift the asset allocation to take advantage of shifts in the performance of the various asset classes. If an investor has the same original portfolio allocation 70%/25%/5% and the portfolio manager thought that the bond market would outperform all other investments, they may use tactical rebalancing to rebalance as follows 40%/55%/5%. Alternatively, Investors may elect to employ a buy and hold strategy and let the allocations go where they may. This buy and hold strategy would reduce transaction costs and tax consequences.