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Investor's Glossary of Terms, Abbreviation, Ratios, Acronyms, Equations and Proper Nouns (some defined here, others linked).

Please note this page is under construction and has not yet been reviewed for errors. Please send suggestions / corrections / comments to aranm@mercuryanalytics.com Last updated 03/13/2001

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

A	Alpha - Used in statistics as a variable for Significance level. May also be used to signify a Type I Error (false positive). Also see Jensen's Measure. Arbitrage - A completely risk free trade. APT (Arbitrage Pricing Theory) - A pricing model for assets, different from CAPM in that it doesn't have restrictive assumptions such as the one that a stock's beta determines its return; APT doesn’t specify the number or even identify the factors that determines a stock's value. A factor with numerical score of zero has no effect on returns, while a negatively scored factor has an inverse impact on returns. Assumes that assets with similar risk reward ratios should be price similarly. As developed by Ross, APT holds that there are several variables, changing over time, that define a firm's value. Autocorrelation - where a variable's value is related to its previous value. A common assumption of time series analysis is that each successive value is independent of its previous value. Avoirdupois - Measurement system commonly used in the US; an avoirdupois ounce is slightly less than a troy ounce. 1 ounce = 28.35 grams (compared to troy ounces at 31.103 grams)
B	Backwardation - the unusual market condition where the spot price is higher than the futures price (follow link for more detail). Opposite of contango. Occurs when the lease rates for the metal are higher than the cost of money (interest rates); backwardation is indicative of high immediate demand for a metal with expectations of easing conditions in the future. Beta - A measure of correlation to market. Divide covariance of an asset by stock's return. May also be used to signify a Type II Error (false negative). Bonds - a tradable debt instrument, typically with bi-annual coupon payments of interest and final payment of principal at the end of the bond's tenure. Some bonds, called zero-coupon bonds, are sold at a discount to the final principle payment, thus reflecting the interest rate value over the bond's tenure. See terms and equations regarding bond Yields, below.
C	CAPM - Capital Asset Pricing Model, the model used to figure what returns are appropriate for an asset's level of risk. The idea is that the riskier the asset is, the more return you should get. Market risk is measured by an asset's risk independent of general market risk, a measurement called "beta." Rr = R(f) - b[R(m)-R(f)] Central Limit Theorem - 1. If population is normally distributed, so to will be the means of samples. 2. If population is large, the means of samples and population will be equal. 3. If population is not normally distributed, means of samples will be approximately normally distributed. Closed and Open-ended funds - Closed end funds are shares whose values are based on NAV and traded on an exchange (regular secondary market), price determined by supply and demand, NAV and market price are almost never same with market price at 5 - 10% discount to NAV; whereas open-ended fund has unlimited number of shares, continuing buying and selling without sales charges. Coefficient of Variation - Standard Deviation divided by arithmetic mean (sample mean) Conversion Price (for a convertible bond) = Cost of convertible bond / conversion ratio Conversion Premium (for a convertible bond) = (conversion price - current stock price) / current stock price Correlation - the degree that movement in one variable is explained by the movement in another (linguistic definitions of correlation sometimes cause controversy, please see the humorous and informative excerpt on the subject from The Economist. Mathematically it's more clear cut: For two variables, X and Y, Correlation = Covariance of X,Y divided by the product of standard deviation of X and the standard deviation of Y). CML - Capital Market Line, represents a combination of investment assets in a portfolio when either borrowing or lending at the risk free rate. A kink can occur if borrowing rate exceeds lending rate. Slope is (MktReturn -Rf) / Mkt. Stddev. It is possible for a particular portfolio to lay above or below the slope. Portfolio is tangent to CML when [Stddev(p) * (Slope of CML)] + Rf = Return expected. If R(p) > return expected, then portfolio is above the CML. Contango - the price relationship between the spot price and the futures contract price, with the futures price being higher than the spot price. The two tend to converge as the contract delivery date approaches. Contango generally recognizes the time value between now and the futures delivery date, as expressed by the going interest rate. Current Ratio - Current assets / current liabilities (an internal liquidity ratio, not an operating performance ratio)
D	Derivative - A financial instrument whose price is based upon the changes in price of an underlying asset. For example, a contract for future delivery of 50 ounces of platinum at $500 two months from now is an agreement that has its own value and can be traded, although that value is based upon the underlying value of the platinum to be delivered. Dividend Discount Model (DDM) - Po = ( D1/k-g); As D1 = Payout ratio * earnings => we can say that Po/E1 = Payout / (k-g); k = required rate of return, g = dividend growth rate Duration - A measure for the price sensitivity of bonds given changes in interest rates. See Modified Duration and Macaulay Duration for equations below.
E	EFP - Exchange for Physical - In cash markets, buyer or sellers may exchange a futures position for a physical position of roughly the same quantity. Used as a means of getting into or out of a futures position prior to the specified contract delivery date. Errors; Type I and Type II - Type I error is rejecting the null hypothesis when it is true (sometimes known as an alpha error), Type II error is accepting the null hypothesis when it is false (sometimes known as a beta error). Minimizing the possibility of a Type II error maximizes the power of a test. Expected Dividend - Payout Ratio x Earnings x growth
F	Futures Contract - A contract for delivery of a specified amount of a commodity at a specified date. A means of reducing price risk for both consumers and producers. Fix - As in "the London Fix", the twice daily price quotation in London for the precious metals. In the case of platinum, the process is described by Standard Bank as that where the chairman announces opening prices to dealers and their customers, who then express their demand levels accordingly. The chairman adjusts the price upwards and downwards in accordance with demand and availability of metal. The price at which the orders are cleared is the Fix.
G
H	Homoscedasticity - related to variance of error term, implies stability Heteroscedasticity - implies instability, fatness of tails in a distribution
I	IRR - Rate that equates PV of cash inflows with PV of cash outflows
J	Jensen's Measure - Also known as Alpha, differential between CAPM and expected return of stock, means firm is underpriced if measure is positive and overpriced if measure is negative. Often used to measure a fund manager's performance. Actual Portfolio Return - Risk Free Return - [Beta * Market Return - Rf]
K
L	LME - London Metals Exchange
M	M1 = One of the national measures of money supply, most narrow; Paper currency, coins, demand deposits, other checkable deposits, non-bank traveler's checks M2 = A more expansive measurement of money supply than M1, includes all Paper currency, coins, demand deposits, other checkable deposits, non-bank traveler's checks (as does M1) plus savings deposits and overnight repurchase agreements (Macaulay) Duration - Price elasticity of a bond. Using Duration to find price change: -Modified Duration (ytm new - YTM old) Price Mode - Most frequently occurring number in a series, would be the highest bar in a histogram (greatest frequency) Modified Duration - Duration / (1+(yield/payments per year) Multicollinearity - high degree of correlation amongst independent variables
N	Net Profit Margin - Net income / net sales (sometimes called "net credit sales") NYMEX - New York Mercantile Exchange, began offering platinum futures in 1956.
O	Option - For the purchaser of an option, an option is the right but not the obligation to buy/sell a specified amount of a commodity at a certain date and at a certain price. The writer of an option collects a premium from the buyer, and is obliged to conform if the purchaser elects to exercise the option. The purchaser will only do so if prices are favorable.
P	Payout Ratio - Earnings / Dividends PEM - Proton Exchange Membrane, the heart of the currently most commercially viable fuel cell designs. Uses a platinum catalyst to combine hydrogen and oxygen into water, with electricity as a byproduct. PGM - Platinum Group Metal, one of six metals (platinum, palladium, rhodium, iridium, osmium, ruthenium) grouped together in the periodic table with similar properties and often found together in nature. Sometimes referred to as PGE, or Platinum Group Element (PGE) P/E Ratio Model - Can be derived from Dividend Discount Model (DDM). Price = Expected Dividend / Required Rate of Return - Expected Growth Rate of Dividends PPP - Purchasing Power Parity, a way to adjust exchange rates to accomodate for relative purchasing power for same goods. The example that follows is an adjustment between US dollars and Pounds, per the famous Big Mac Index in the Economist. P US = [ R($/ £)]*P UK
Q	Quick, or Acid-Test Ratio - Same as Current Ratio, but that inventories and pre-paid expenses are excluded in the Quick Ratio
R	Reserves - (mining) Proven tonnage and grade ore that can be mined profitably. Resources - (mining) Identified ore body, with no certainty attached regarding the profitability of working the ore. A mine's stated resources are usually larger than its reserves.
S	Sampling Error - the difference between the sample mean and the population mean. Sharpe Valuation of a Portfolio - Portfolio performance measure accounting for risk; S = Rp - Rf / Sd(p), where Rp is return of portfolio and Sd(p) is the standard deviation of a portfolio. Significance Level - Statistical measure of probability of a test statistic being acceptable (usual value = 95%, t = 2), represented with the greek letter alpah SML - Security Market Line, the SML measures performance of a particular security's expected return as a function of its systematic risk, or beta - as opposed to its standard deviation. (Return is Y axis, Beta is X axis, Rf is Y intercept, slope risk-reward tradeoff) Use CAPM to judge whether a portfolio is on SML or no. Spot - As in "spot prices", meaning cash price. Note that there is no uniform, singular "spot price" for a given commodity, it is a figure quoted by a particular buyer in a particular place. Arbitrage helps to push prices to uniformity across distance, but some structural or market peculiarities may at times inhibit the arbitrage mechanism.
T	Tobin's Q - The ratio of a firm's market value (or market capitalization, # of shares outstanding x price per share) to the replacement value of its assets; ie market value / replacement cost. Used by some as a measure whether a stock is correctly priced, with the theory being that a firm in the long run should not be valued more than the replacement value of its assets. TOCOM - Tokyo Commodities Exchange, began trading in platinum in 1984. The world's most active market for platinum trading, as Japan is the world's largest consumer of platinum. Treynor Portfolio Performance Measure - T = (Rp - Rf) / b(p), where b(p) = beta of portfolio, Rp = return on portfolio, Rf = risk free rate Troy - an archaic weight measurement conventionally used in the precious metals industry. Prices quoted in ounces are quoted in ounces troy, a troy ounce being heavier than a standard (avoirdupois) ounce. 1 ounce troy weighs 31.103 grams
U
V
W
X
Y	Yields - For Bonds, Current Yield = Coupon / current price; Nominal yield = coupon rate; Effective yield yield based on future sale value (not known until future); and YTM Horizon returns for bonds: Yield achieved by buying, holding, and selling bond, need purchase and sale price to calculate. Effective annual yield for bonds = [(1 + yield) ^2] - 1 . Holding Period Yield = (Ending Value - Beginning Value) / Beginning Value.
Z	Z-Value - [X - Mean / Standard Deviation], used for predicting likelihood of certain value's outcome given above figures

Some common finance terms, ratios, and models below. PLEASE NOTE THIS IS STILL UNDER CONSTRUCTION.

2. P/E = Payout Ratio / (Expected Return on asset - Growth Rate, or, k-g) solve for k using CAPM (note that required - or expected - return on asset is different from market rate of return)

3. Compounded growth rate = principal * (1+g) ^ n

4. Simple P/E Ratio: Share Price / EPS

7. Multiple growth model yield [Example for change of growth rate after n years] Y1 Dividend / (1 + required rate of return)^1 + Y2 Dividend / (1 + required rate of return)^2 + Y3 Dividend / (1 + required rate of return)^3 + ... Yn Dividend / (1 + required rate of return)^n + Yn Stock price/ (1 + required rate of return)^n. Be sure to grow dividend at appropriate rate.

8. Market Capitalization Rate = Required Rate of Return (synonymous)

10. Alpha - Returns greater than the risk-adjusted required return (such as is derived using CAPM), the y-intercept

11. Sustainable Growth Model: Company's future growth rate = g = ROE*b, where b = retention ratio. Note: don't forget that retention ratio = 1-dividend payout ratio

12. ROE = Net Income / Equity (expressed in $ terms)

13. Total Asset Turnover = Net Sales / Total Average Assets

16. Conversion Ratio = Convertible Security Par Value / Conversion Price of Stock (Conversion ratio x current stock price is generally considered downward limit for price of convertible security)

18. Book Value per share = common equity / # of shares outstanding

19. DuPont System (traditional): Dividing ROE into 3 categories - Net Income to Sales (indicating profit margin), Sales to Total Assets (indicating asset turnover and how well assets are utilized), and Total Assets to Common Equity (representing a firm's leverage).

21. Bond Immunization: The technique of ensuring that a change in a bond portfolio's value due to interest rate changes is offset by a change in the portfolio's interest rate income; offsetting is achieved by investing in bonds that have a duration equal to the investment horizon of the investor.

22. Dividend Discount Model - div/r-g; where r = required rate of return, g = expected growth rate of dividends, div = next year's dividend; should equal price of share

23. Calculating capital lease expenses: take NPV of lease less salvage, divided over lease term, for straight line depreciation expense; plus present value of lease times interest rate

24. PBO = Projected Benefit Obligation, based on expected future compensation, ABO = Accumulated Benefit Obligation, based on prior future compensation, also know Vested Benefits Obligation

25. Depreciation Methods - Accelerated: Declining Balance and sum-of-the-years-digits, Straight Line: Units-of-production and service-hour methods. Be aware of a "half-year convention" where the asset is put into service half way - or anytime - through the year can be counted for the whole year.

26. Pretax Cost of Debt = Yield to Maturity of Bond

27. 43. YTM = [CouponPymt + [(FV-PV)/ Years Remaining]]/[FV+PV/2]

28. EPS = Earnings - Preferred Dividends / Shares outstanding

29. Modigliani-Miller Model of Firm Valuation = Take Cashflow before interest and taxes and divide by required rate of return. Assumes no taxes; RE = RA + (RA-RD)x(D/E), RE is return on equity, RA is req. rate of return on assets, RD is return on debt, D/E is debt equity.

31. Operating Leverage - Percentage change in earnings before interest and taxes divided by percentage change in sales.

32. 4 types of dividends: Stock dividends, Property dividends, Cash dividends, Liquidating dividends. All reduce shareholder's equity except stock dividends, which effect only composition of equity.

33. Three major activities on Statement of Cashflows: Operating, Financing, and Investing activities

34. Common-size Financial Statements take balance sheet and income statement entries, divide them by total assets or total sales respectively, and express all items in terms of percentages.

35. Auditor's Opinions on Financial Statements: Adverse - Report does not accurately characterize firm's financial performance or position, Qualified - approves all but specified items, Unqualified - reports fairly represent a firm's financial performance and position, Disclaimer - Insufficient information

36.

37. Inventory Turnover Ratio = COGS / Average Inventory

38. Working Capital = Current Assets - Current Liabilities

39. Strict Residual Dividend Policy - Means that only residual earnings not put towards capital spending must be dividended out. Therefore, internally generated equity / ratio of equity to value = max amount of capital investment, at zero dividend, without issuing new equity.

40. Interest Rate Parity = spot * ratio; ratio is (1+foreign i / 1+local i)

46. CONVERSION FOR ANNUITY DUE - For payment streams where a payment is made / received right off the bat (at beginning of period) take NPV and multiply by 1+r.

47. Annuity PV factor = [1-(1/(1+r))^t]/r; If regular annuity, take Annuity PV factor and multiply by period payment amounts to get PV; that is, (Payment $)*(Annuity PV factor) = PV

48.

52. Standard Deviation = Square root of variance, dispersion of actual values of dependent variable around line of regression (as opposed to standard error of estimate, which measures dispersion of observed values of dependent variable around line of regression) Calculating Standard Deviation: Fill out columns below for values given (typically starting with probability scenarios and associated returns).

X P(X) X-E(X) [X-E(X)]* (*means squared) [X-E(X)]* P(X)

Sum the last column for Variance, take square root

For a series with probabilities P, use equation below:

54. Measure of Central Tendency - A single value which represents a set of data, Mean (arithmetic and geometric), Median, Mode are examples of such a measure

56. Discrete Random Variable - One that can assume only a finite, clearly separated set of values within a defined range

57. Standard Error of the Sample Means = Standard Deviation / Square root of sample size

58.

59. Probability of one event given another: P of (A and B) = P of A x P of (B|A)

60. Calculating Standard Error of the Sample Means = Standard Deviation / Square root of sample size (that is, population of sample)

62. Class interval = (Highest value - lowest value) / # of classes

63. Variance = Sum of all (Probability * (Return - Expected Return))^2, OR, Variance = Sum the square of each observation's difference from the mean, and divide by # of observations (population variance) or # of observations minus one for sample variance.

66. Firm-specific risk = 1-[(Corr to index)^2)], leave out the "1 minus" calc to derive explaining power of correlated statistic

67. R-square on a simple regression measures extent to which variance in the independent variable explains variance in the dependent variable, found by squaring the correlation coefficient.

68. T-Value, T-Test, T-test statistic: for difference between means, with equal population variances and independent samples, used to calculate confidence intervals for µ, (See stats text on page 309 for historical note on Gosset, who invented it while working for Guinness) Most useful for estimating the probable error of the mean for small samples.

69. T-test values greater than 2 imply that the null hypothesis should be rejected. Null hypothesis is typically set to zero, T-test value does not say whether greater or less than zero; similar to significance threshold of 5%; signifies higher probability than expressed by chance.

72. Covariance - What is difference between Variance and Covariance? Variance is measure of a distribution's typical departure from the mean; Covariance is statistical relationship between two distributions

76. Two-stock portfolio variance for A,B[(W(A)^2)*(StDev(A)^2)]+[(W(B)^2)*(StDev(B)^2)]+[2*W(A)*W(B)*Cov(AB)]To get StDev of portfolio, take square root of this number

Compiled by Aran Murphy. Please send corrections, additions or comments to me at economist@platinumguild.org or aran@murphybrothers.org

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