Chapter 1: The Investment Setting

Arithmetic Mean

A mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series. The arithmetic mean is sometimes referred to as the average or simply as the mean. Some mathematicians and scientists prefer to use the term "arithmetic mean" to distinguish it from other measures of averaging, such as the geometric mean and the harmonic mean. http://www.investopedia.com/terms/a/arithmeticmean.asp#ixzz4I6d3KknA

Risk

Involves the chance an investment's actual return will differ from the expected return. Risk includes the possibility of losing some or all of the original investment. Different versions of risk are usually measured by calculating the standard deviation of the historical returns or average returns of a specific investment. Read more: http://www.investopedia.com/terms/r/risk.asp#ixzz4I6mhuncU

Expected Return

The amount of profit or loss an investor anticipates on an investment that has various known or expected rates of return. It is calculated by multiplying potential outcomes by the chances of them occurring, and summing these results. For example, if an investment has a 50% chance of gaining 20% and a 50% change of losing 10%, the expected return is (50% x 20% + 50% x -10%), or 5%. BREAKING DOWN 'Expected Return' Expected return is usually based on historical data and is not guaranteed. For the most part, the expected return is a tool used to determine whether or not an investment has a positive or negative average net outcome. In the example above, for instance, the 5% expected return may never be realized in the future; it is merely an average of what may occur. In addition to expected return, wise investors should also consider the probability of return in order to properly assess risk. After all, one can find instances in which certain lotteries offer a positive expected return, despite the very low probability of realizing that return. Expected Return of a Portfolio The expected return doesn't just apply to single investments. It can also be analyzed for a portfolio containing many investments. If the expected return for each investment is known, the portfolio's overall expected return is simply a weighted average of the expected returns of its components. For example, assume the following portfolio of stocks: Stock A: $500,000 invested and an expected return of 15% Stock B: $200,000 invested and an expected return of 6% Stock C: $300,000 invested and an expected return of 9% With a total portfolio value of $1,000,000, the weight's of Stock A, B and C are 50%, 20% and 30%. Thus, the expected return of the total portfolio is: Expected return of portfolio = (50% x 15%) + (20% x 6%) + (30% x 9%) = 7.5% + 1.2% + 2.7% = 11.4% Risk Must Also Be Analyzed It is quite dangerous to make investment decisions based on expected returns alone. Investors should always review the risk characteristics of investment opportunities before making any buying decisions, to determine if the investments align with their portfolio goals. For example, assume two hypothetical investments exist. Their annual performance results for the last five years are: Investment A: 12%, 2%, 25%, -9%, 10% Investment B: 7%, 6%, 9%, 12%, 6% Both of these investments have expected returns of exactly 8%. But when analyzing the risk of each, as defined by standard deviation, Investment A is approximately five times more risky than Investment B (Investment A has a standard deviation of 12.6% and Investment B has a standard deviation of 2.6%). Read more: Expected Return Definition | Investopedia http://www.investopedia.com/terms/e/expectedreturn.asp#ixzz4I6ioqoHJ

Geometric Mean

The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio. It is technically defined as "the 'n'th root product of 'n' numbers." The geometric mean must be used when working with percentages, which are derived from values, while the standard arithmetic mean works with the values themselves. Geometric Mean If you have $10,000 and get paid 10% interest on that $10,000 every year for 25 years, the amount of interest is $1,000 every year for 25 years, or $25,000. However, this does not take the interest into consideration. That is, the calculation assumes you only get paid interest on the original $10,000, not the $1,000 added to it every year. If the investor gets paid interest on the interest, it is referred to as compounding interest, which is calculated using the geometric mean. Using the geometric mean allows analysts to calculate the return on an investment that gets paid interest on interest. This is one reason portfolio managers advise clients to reinvest dividends and earnings. The geometric mean is also used for present value and future value cash flow formulas. The geometric mean return is specifically used for investments that offer a compounding return. Going back to the example above, instead of only making $25,000 on a simple interest investment, the investor makes $108,347.06 on a compounding interest investment. Simple interest or return is represented by the arithmetic mean, while compounding interest or return is represented by the geometric mean. Geometric Mean Calculation To calculate compounding interest using the geometric mean, the investor needs to first calculate the interest in year one, which is $10,000 multiplied by 10%, or $1,000. In year two, the new principal amount is $11,000, and 10% of $11,000 is $1,100. The new principal amount is now $11,000 plus $1,100, or $12,100. In year three, the new principal amount is $12,100, and 10% of $12,100 is $1,210. At the end of 25 years, the $10,000 turns into $108,347.06, which is $98,347.05 more than the original investment. The shortcut is to multiply the current principal by one plus the interest rate, and then raise the factor to the number of years compounded. The calculation is $10,000 × (1+0.1) 25 = $108,347.06. http://www.investopedia.com/terms/g/geometricmean.asp#ixzz4I6eEuV19

Investment

The current commitment of dollars for a period of time in order to derive future payments that will compensate the investor for (1) the time the funds are committed, (2) the expected rate of inflation during this time period, an (3) the uncertainty of the future payments.

Yield

The income return on an investment, such as the interest or dividends received from holding a particular security. The yield is usually expressed as an annual percentage rate based on the investment's cost, current market value or face value. Yields may be considered known or anticipated depending on the security in question as certain securities may experience fluctuations in value. BREAKING DOWN 'Yield' The yield of an investment is tied to the risk associated with the aforementioned investment. The higher the risk is considered to be, the higher the associated yield potential. Except in the most secure investments, such as zero coupon bonds, a yield is not a guarantee. Instead, the listed yield is functionally an estimate of the future performance of the investment. Generally, the risks associated with stocks are considered higher than those associated with bonds. This can lead stocks to have a higher yield potential when compared to many bonds currently on the market. Stock Yields In regards to a stock, there are two stock dividend yields. If you buy a stock for $30 (cost basis) and its current price and annual dividend are $33 and $1, respectively, the cost yield will be 3.3% ($1/$30) and the current yield will be 3% ($1/$33). Bond Yields Bonds have multiple yield options depending on the exact nature of the investment. The coupon is the bond interest rate fixed at issuance. The current yield is the bond interest rate as a percentage of the current price of the bond. The yield to maturity is an estimate of what an investor will receive if the bond is held to its maturity date. Non-taxable municipal bonds will also have a tax-equivalent (TE) yield determined by the investor's tax bracket. Mutual Fund Yields Mutual funds have two primary forms of yields for consideration. The dividend yields are expressed as an annual percentage measure of the income that was earned by the fund's portfolio. The associated income is derived from the dividends and interest generated by the included investments. Additionally, dividend yields are based on the net income received after the fund's associated expenses have been paid, or at a minimum, accounted for. The SEC yield is based on the yields reported by particular companies as required by the Securities and Exchange Commission (SEC) and is based on an assumption that all associated securities are held until maturity. Additionally, the assumption exists that all income generated is reinvested. Like dividend yields, SEC yields also account for the presence of required fees associated with the fund, and allocates funds to them accordingly before determining the actual yield. Read more: Yield Definition | Investopedia http://www.investopedia.com/terms/y/yield.asp#ixzz4I6TCOidl

Required Rate of Return (RRR)

The minimum annual percentage earned by an investment that will induce individuals or companies to put money into a particular security or project. The RRR is used in both equity valuation and in corporate finance. Investors use the RRR to decide where to put their money, and corporations use the RRR to decide if they should pursue a new project or business expansion. http://www.investopedia.com/terms/r/requiredrateofreturn.asp#ixzz4I6PzTAr6

Holding Period Return (HPR) & Holding Period Yield (HPY)

The total return received from holding an asset or portfolio of assets over a period of time, generally expressed as a percentage. Holding period return/yield is calculated on the basis of total returns from the asset or portfolio - i.e. income plus changes in value. It is particularly useful for comparing returns between investments held for different periods of time. 1. What is the HPR for an investor who bought a stock a year ago at $50 and received $5 in dividends over the year, if the stock is now trading at $60? HPR = [5 + (60 - 50)] / 50 = 30% 2. Which investment performed better? Mutual Fund X that was held for three years, during which it appreciated from $100 to $150 and provided $5 in distributions, or Mutual Fund B that went from $200 to $320 and generated $10 in distributions over four years? HPR for Fund X = [5 + (150 - 100)] / 100 = 55% HPR for Fund B = [10 + (320 - 200)] / 200 = 65% Note that Fund B had the higher HPR, but it was held for four years, as opposed to the three years for which Fund X was held. Since the time periods are different, this requires annualized HPR to be calculated, as shown below. 3. Calculation of annualized HPR: Annualized HPR for Fund X = (0.55 + 1)1/3 - 1 = 15.73% Annualized HPR for Fund B = (0.65 + 1)1/4 - 1 = 13.34% Thus, despite having the lower HPR, Fund X was clearly the superior investment. 4. Your stock portfolio had the following returns in the four quarters of a given year: +8%, -5%, +6%, +4%. How did it compare against the benchmark index, which had total returns of 12% over the year? HPR for your stock portfolio = [(1 + 0.08) x (1 - 0.05) x (1 + 0.06) x (1 + 0.04)] - 1 = 13.1% Your portfolio therefore outperformed the index by more than a percentage point (however, the risk of the portfolio should also be compared to that of the index to evaluate if the added return was generated by taking significantly higher risk). http://www.investopedia.com/terms/h/holdingperiodreturn-yield.asp#ixzz4I6RYP0tg

Variance

a measurement of the spread between numbers in a data set. The variance measures how far each number in the set is from the mean. Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set. X: individual data point u: mean of data points N: total # of data points Note: When calculating a sample variance to estimate a population variance, the denominator of the variance equation becomes N - 1 so that the estimation is unbiased and does not underestimate population variance. Read more: Variance Definition | Investopedia http://www.investopedia.com/terms/v/variance.asp#ixzz4I6o84cU4