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Chapter 9. How to deflect and roll with the punches.

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CFO. CFO does not include cash outlays for replacing old equipment. Free Cash Flow (FCF) is intended to measure the cash available to a company for discretionary uses after making all required cash outlays. <span>It accounts for capital expenditures and dividend payments, which are essential to the ongoing nature of the business. The basic definition is cash from operations less the amount of capital expenditures required to maintain the company's present productive capacity. &#

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3; The basic definition is cash from operations less the amount of capital expenditures required to maintain the company's present productive capacity. Free cash flow = CFO - capital expenditure <span>Free Cash Flow to the Firm (FCFF): Cash available to shareholders and bondholders after taxes, capital investment, and WC investment. FCFF = NI + NCC + Int (1 - Tax rate) - FCInv - WCInv NI: Net income available to common shareholders. It is the com

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; Free cash flow = CFO - capital expenditure Free Cash Flow to the Firm (FCFF): Cash available to shareholders and bondholders after taxes, capital investment, and WC investment. <span>FCFF = NI + NCC + Int (1 - Tax rate) - FCInv - WCInv NI: Net income available to common shareholders. It is the company's earnings after interest, taxes and preferred dividends. NCC: Net non-cash

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; Free cash flow = CFO - capital expenditure Free Cash Flow to the Firm (FCFF): Cash available to shareholders and bondholders after taxes, capital investment, and WC investment. <span>FCFF = NI + NCC + Int (1 - Tax rate) - FCInv - WCInv NI: Net income available to common shareholders. It is the company's earnings after interest, taxes and preferred dividends. NCC: Net non-cash

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The time value of money (TVM) refers to the fact that $1 today is worth more than $1 in the future. This is because the $1 today can be invested to earn interest immediately. The TVM reflects the relationship between present value, future value, time, and interest rate. The time value of money underlies rates of return, interest rates, required rates of retu

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The time value of money (TVM) refers to the fact that $1 today is worth more than $1 in the future. This is because the $1 today can be invested to earn interest immediately. The TVM reflects the relationship between present value, future value, time, and interest rate. The time value of money underlies rates of return, interest rates, required rates of return, discount rates, opportunity costs, inflation, and risk. It reflects the relationship between

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interest rate. The time value of money underlies rates of return, interest rates, required rates of return, discount rates, opportunity costs, inflation, and risk. It reflects the relationship between time, cash flow, and interest rate. <span>There are three ways to interpret interest rates: Required rate of return is the return required by investors or lenders to postpone their current consumption. Discount rate is the rate used to discount future cash flows

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n, interest rates, required rates of return, discount rates, opportunity costs, inflation, and risk. It reflects the relationship between time, cash flow, and interest rate. There are three ways to interpret interest rates: <span>Required rate of return is the return required by investors or lenders to postpone their current consumption. Discount rate is the rate used to discount future cash flows to allow for the time value of money (that is, to bring a future value equivalent to present value). Opportunity cost is the

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e return required by investors or lenders to postpone their current consumption. Discount rate is the rate used to discount future cash flows to allow for the time value of money (that is, to bring a future value equivalent to present value). <span>Opportunity cost is the most valuable alternative investors give up when they choose what to do with money. In a certain world, the interest rate is called the risk-free rate. For investors preferring current to future consumption, the risk-free interest rate is the rate of compensation

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licate interest rates: Inflation: When prices are expected to increase, lenders charge not only an opportunity cost for postponing consumption but also an inflation premium that takes into account the expected increase in prices. <span>The nominal cost of money consists of the real rate (a pure rate of interest) and an inflation premium. Risk: Companies exhibit varying degrees of uncertainty concerning their ability to repay lenders. Lenders therefore charge interest rates that incorporate default

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nominal risk-free rate (real rate + an inflation premium) and a default risk premium. Compounding is the process of accumulating interest over a period of time. A compounding period is the number of times per year that interest is paid. <span>Continuous compounding occurs when the number of compounding periods becomes infinite; interest is added continuously. Discounting is the calculation of the present value of some known future value. Discount rate is the rate used to calculate the present value of some future cash flow. Disco

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per year that interest is paid. Continuous compounding occurs when the number of compounding periods becomes infinite; interest is added continuously. Discounting is the calculation of the present value of some known future value. <span>Discount rate is the rate used to calculate the present value of some future cash flow. Discounted cash flow is the present value of some future cash flow. <span><body><html>

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ding periods becomes infinite; interest is added continuously. Discounting is the calculation of the present value of some known future value. Discount rate is the rate used to calculate the present value of some future cash flow. <span>Discounted cash flow is the present value of some future cash flow. <span><body><html>

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licate interest rates: Inflation: When prices are expected to increase, lenders charge not only an opportunity cost for postponing consumption but also an inflation premium that takes into account the expected increase in prices. <span>The nominal cost of money consists of the real rate (a pure rate of interest) and an inflation premium. Risk: Companies exhibit varying degrees of uncertainty concerning their ability to repay lenders. Lenders therefore charge interest rates that incorporate default

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le. Reinvestment The IRR is intended to provide a single number that represents the rate of return generated by a capital investment. As such, it is an easy number to interpret and understand. However, calculation of <span>the IRR assumes that all project cash flows can be reinvested to earn a rate of return exactly equal to the IRR itself. In other words, a project with an IRR of 6% assumes that all cash flows can be reinvested to earn exactly 6%. If the cash flows are invested at a rate lower than 6%, the realized return

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usive projects of greatly differing scale: one that requires a relatively small investment and returns relatively small cash flows, and another that requires a much larger investment and returns much larger cash flows. <span>Timing The other situation in which IRR is likely to contradict NPV is when there are two mutually-exclusive projects whose cash flows are timed very differently: one that receives its

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When analyzing rates of return, our starting point is the total return, or holding period return (HPR). HPR measures the total return for holding an investment over a certain period of time, and can be calculated using the following formula:

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When analyzing rates of return, our starting point is the total return, or holding period return (HPR). HPR measures the total return for holding an investment over a certain period of time, and can be calculated using the following formula:

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When analyzing rates of return, our starting point is the total return, or holding period return (HPR). HPR measures the total return for holding an investment over a certain period of time, and can be calculated using the following formula: P t = price per share at the end of time period t P (t-1) = price per share at the

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When analyzing rates of return, our starting point is the total return, or holding period return (HPR). HPR measures the total return for holding an investment over a certain period of time, and can be calculated using the following formula: P t = price per share at the end of time period t P (t-1) = price per share at the end of time period t-1, the time period immediately

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The dollar-weighted rate of return is essentially the internal rate of return (IRR) on a portfolio. This approach considers the timing and amountof cash flows. It is affected by the timing of cash flows. If funds are added to a portfolio when the portfolio is performing well (poorly),

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rs the timing and amountof cash flows. It is affected by the timing of cash flows. If funds are added to a portfolio when the portfolio is performing well (poorly), the dollar-weighted rate of return will be inflated (depressed). <span>The time-weighted rate of return measures the compound growth rate of $1 initial investment over the measurement period. Time-weightedmeans that returns are averaged over time. This approach is not affected by the timing of cash flows; therefore, it is the preferred method of performance measurement. 

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For the second year, HPR 2 : (280 + 20)/300 - 1 = 0. Calculate the time-weighted rate of return: If the measurement period < 1 year, compound holding period returns to get an annualized rate of return for the year. <span>If the measurement period > 1 year, take the geometric mean of the annual returns. <span><body><html>

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unt basis D = the dollar discount, which is equal to the difference between the face value of the bill, F, and its purchase price, P t = the number of days remaining to maturity 360 = the bank convention of the number of days in a year. <span>Bank discount yield is not a meaningful measure of the return on investment because: It is based on the face value, not on the purchase price. Instead, return on investment should be measured based on cost of investment. It is annualized using a 360-day year, not a 365-day year. It annualizes with simple interest and ignores the effect of interest on interest (compound interest). Holding period yield (HPY) is the return earned by an investor if the money market instrument is held until maturity: P 0 =

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unt basis D = the dollar discount, which is equal to the difference between the face value of the bill, F, and its purchase price, P t = the number of days remaining to maturity 360 = the bank convention of the number of days in a year. <span>Bank discount yield is not a meaningful measure of the return on investment because: It is based on the face value, not on the purchase price. Instead, return on investment should be measured based on cost of investment. It is annualized using a 360-day year, not a 365-day year. It annualizes with simple interest and ignores the effect of interest on interest (compound interest). Holding period yield (HPY) is the return earned by an investor if the money market instrument is held until maturity: P 0 =

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unt basis D = the dollar discount, which is equal to the difference between the face value of the bill, F, and its purchase price, P t = the number of days remaining to maturity 360 = the bank convention of the number of days in a year. <span>Bank discount yield is not a meaningful measure of the return on investment because: It is based on the face value, not on the purchase price. Instead, return on investment should be measured based on cost of investment. It is annualized using a 360-day year, not a 365-day year. It annualizes with simple interest and ignores the effect of interest on interest (compound interest). Holding period yield (HPY) is the return earned by an investor if the money market instrument is held until maturity: P 0 =

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990. Bank discount yield: (1000 - 990)/1000 x 360/60 = 6% Holding period yield: (1000 - 990)/990 = 1.0101% Effective annual yield: (1 + 1.0101%) 365/60 - 1 = 6.3047% Money market yield: (360 x 6%)/(360 - 60 x 6%) = 6.0606% <span>If we know HPY, then: EAY = (1 + HPY) 365/t - 1 r MM = HPY x 360/t If we know EAY, then: HPY = ( 1 + EAY) t/365 - 1 r MM = [(1 + EAY) t/365 - 1] x (360/t) If we know r MM , then: HPY = r MM x (t/360) EAY = (1 + r

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ld: (360 x 6%)/(360 - 60 x 6%) = 6.0606% If we know HPY, then: EAY = (1 + HPY) 365/t - 1 r MM = HPY x 360/t If we know EAY, then: HPY = ( 1 + EAY) t/365 - 1 r MM = [(1 + EAY) t/365 - 1] x (360/t) <span>If we know r MM , then: HPY = r MM x (t/360) EAY = (1 + r MM x t/360) 365/t - 1 <span><body><html>

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Periodic bond yields for both straight and zero-coupon bonds are conventionally computed based on semi-annual periods, as U.S. bonds typically make two coupon payments per year. For example, a zero-coupon bond with a maturity of five years will mature in 10 6-month periods. The periodic yield for that bond, r, is indicated by the equation Price = Maturity value

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y. This method ignores the effect of compounding semi-annual YTM, and the YTM calculated in this way is called a bond-equivalent yield (BEY). However, yields of a semi-annual-pay and an annual-pay bond cannot be compared directly <span>without conversion. This conversion can be done in one of the two ways: Convert the bond-equivalent yield of a semi-annual-pay bond to an annual-pay bond.

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#13; Since a pure discount instrument (e.g., a T-bill) makes no interest payment, its HPY is (P 1 - P 0 )/P 0 . Note that HPY is computed on the basis of purchase price, not face value. It is not an annualized yield. <span>The effective annual yield is the annualized HPY on the basis of a 365-day year. It incorporates the effect of compounding interest. Money market yield (also known as CD equivalent yield) is the annualized HPY on the basis of

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The money-weighted rate of return has a serious drawback. Generally, clients determine when money is given to the investment manager and those decisions may significantly influence the money-weighted rate of return .

The money-weighted rate of return has a serious drawback. Generally, clients determine when money is given to the investment manager and those decisions may significantly influence the money-weighted rate of return . A general principle of evaluation, however, is that a person or entity should be judged only on the basis of their own actions, or actions under their control. An evaluation tool should

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where the returns are centered (central tendency); how far returns are dispersed from their center (dispersion); whether the distribution of returns is symmetrically shaped or lopsided (skewness); and 

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where the returns are centered (central tendency); how far returns are dispersed from their center (dispersion); whether the distribution of returns is symmetrically shaped or lopsided (skewness); and whether extreme outcomes are likely (kurtosis).

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unt basis D = the dollar discount, which is equal to the difference between the face value of the bill, F, and its purchase price, P t = the number of days remaining to maturity 360 = the bank convention of the number of days in a year. <span>Bank discount yield is not a meaningful measure of the return on investment because: It is based on the face value, not on the purchase price. Instead, return on investment should be measured based on cost of investment. It is annualized using a 360-day year, not a 365-day year. It annualizes with simple interest and ignores the effect of interest on interest (compound interest). Holding period yield (HPY) is the return earned by an investor if the money market instrument is held until maturity: P 0 =

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y’s EPS for FY2014 beating $0.69 are 1 to 7 means that the speaker believes the probability of the event is 1/(1 + 7) = 1/8 = 0.125. Odds against E = [1 − P(E)]/P(E), the reciprocal of odds for E. <span>Given odds against E of “a to b,” the implied probability of E is b/(a + b). The statement that the odds against the company’s EPS for FY2014 beating $0.69 are 15 to 1 is consistent with a belief that the probability of the event is

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se price, not face value. It is not an annualized yield. The effective annual yield is the annualized HPY on the basis of a 365-day year. It incorporates the effect of compounding interest. <span>Money market yield (also known as CD equivalent yield) is the annualized HPY on the basis of a 360-day year using simple interest. Example An investor buys a $1,000 face-value T-bill due in 60 days at a price of $990. Bank discount yield: (1000 - 990

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t":"Math Goodies","th":98,"tu":"https://encrypted-tbn0.gstatic.com/images?q\u003dtbn:ANd9GcQcW8yGVex34TZK0u33zmGPrJUYi4Sw9vz1DI4e1YYbbQn3bEVPNVAGcXN2","tw":216} In probability theory, <span>the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment. A sample space is usually denoted using set notation, and the possible ordered outcomes are listed as elements in the set. Sample space - Wikipedia https://en.wikipedia.org/wiki/Sam

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The complement of event A is the event that A does not occur. It is expressed as A c . The probabilities of an event and its complement must have a sum of 1: P(A) + P(A c ) = 1. Note that event A and its complement, A c , are mutually exclusive (t

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The complement of event A is the event that A does not occur. It is expressed as A c . The probabilities of an event and its complement must have a sum of 1: P(A) + P(A c ) = 1. Note that event A and its complement, A c , are mutually exclusive (there is no overlapping

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P(A or B) = P(A) + P(B) - P(AB) The logic behind this formula is that when P(A) and P(B) are added, the occasions on which A and B both occur are counted twice. To adjust for this, P(AB) is subtracted. <span>If events A and B are mutually exclusive, the joint probability of A and B is 0. Consequently, the probability that either A or B occurs is simply the sum of the unconditional probabilities of A and B: P (A or B) = P(A) + P(B). What is the probability t

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Two events, A and B, are independent if and only if P(A|B) = P(A), or equivalently, P(B|A) = P(B). That is, the occurrence of one event has no influence on the probability of the occurrence of the other event. In more detail, whether or not B occurs will have no effect on

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nd B both occur is: P(A and B) = P(A) x P(B) In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B. This relationship is known as the <span>multiplication rule for independent events. What is the probability that a fair coin will come up with heads twice in a row? Two events must occur: heads on the first toss and heads on the second toss. Since the prob

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in the deck, the probability of the first event is 1/52. Since 13/52 = 1/4 of the deck is composed of clubs, the probability of the second event is 1/4. Therefore, the probability of both events is: 1/52 x 1/4 = 1/208. Similarly, <span>for any number of independent events E 1 , E 2 .....E n , the probability that all of them occur is: P(E 1 and E 2 ..... and E n ) = P(E 1 ) x P(E 2 ) x ..... x P(E n ) Example In a bullish market, three shares, chosen from different sectors of the market, have probabilities of 0.6, 0.5 and 0.8 that their share prices will ris

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If we have an event or scenario S, the event not-S, called the complement of S, is written S C . Note that P(S) + P(S C ) = 1, as either S or not-S must occur. The total probability rule explains the unconditional probability of an event in terms of probabilities conditional on the scenarios. P(A) = P(A|S)P(S) + P(A|S C )P(S C ) P(A) = P(A|S 1 )P(S 1 ) + P(A|S 2 )P(S 2 ) + ... + P(A|S n )P(S n ) The first equation is just a special case of the secon

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40,000 + 24,000 + 0 = $64,000 Thus, the organizers can expect to take in $64,000. Since it costs $50,000 to stage the event, this translates to a profit of $14,000, so they should certainly go ahead with the venture. <span>It's important to realize that none of the outcomes actually produces an amount of $64,000. This is simply the weighted average of all possible outcomes. Although there is a 50% chance of a loss the big profit that will be made the remaining 50% of the time more than offsets t

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If we have two events, A and B, that we are interested in, we often want to know the probability that either A or B occurs. Note the use of the word "or," the key to this rule. The "or" is what we call an "inclusive or." In other words, either one event can occur or both events can occur.

If we have two events, A and B, that we are interested in, we often want to know the probability that either A or B occurs. Note the use of the word "or," the key to this rule. The "or" is what we call an "inclusive or." In other words, either one event can occur or both events can occur. Such probabilities are calculated using the addition rule for probabilities. P(A or B) = P(A) + P(B) - P(AB) The logic behind this f

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Facts about covariance: Covariance of returns is negative if, when the return on one asset is above its expected value, the return on the other asset is below its expected value (an average inverse relationship between returns). <span>Covariance of returns is 0 if returns on the assets are unrelated. Covariance of returns is positive if, when the return on one asset is above its expected value, the return on the other asset is above its expected value (an average positive relationsh

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tive if, when the return on one asset is above its expected value, the return on the other asset is below its expected value (an average inverse relationship between returns). Covariance of returns is 0 if returns on the assets are unrelated. <span>Covariance of returns is positive if, when the return on one asset is above its expected value, the return on the other asset is above its expected value (an average positive relationship between returns). The covariance of a random variable with itself (own covariance) is its own variance. Example Suppose that the future short-term outlook for the economy is favorable w

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returns on the assets are unrelated. Covariance of returns is positive if, when the return on one asset is above its expected value, the return on the other asset is above its expected value (an average positive relationship between returns). <span>The covariance of a random variable with itself (own covariance) is its own variance. Example Suppose that the future short-term outlook for the economy is favorable with a probability 0.6 and unfavorable with a probability of 0.4. For two stocks, F and

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where. The correlation between two random variables, R i and R j , is defined as: Alternative notations are corr(R i , R j ) and ρ ij . Properties of correlation: <span>Correlation is a number between -1 and +1. A correlation of 0 indicates an absence of any linear (straight-line) relationship between the variables. Increasingly positive correlation indicates an increasingly strong positive lin

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two random variables, R i and R j , is defined as: Alternative notations are corr(R i , R j ) and ρ ij . Properties of correlation: Correlation is a number between -1 and +1. <span>A correlation of 0 indicates an absence of any linear (straight-line) relationship between the variables. Increasingly positive correlation indicates an increasingly strong positive linear relationship (up to 1, which indicates a perfect linear relationship). Increasingly negative correlati

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otations are corr(R i , R j ) and ρ ij . Properties of correlation: Correlation is a number between -1 and +1. A correlation of 0 indicates an absence of any linear (straight-line) relationship between the variables. <span>Increasingly positive correlation indicates an increasingly strong positive linear relationship (up to 1, which indicates a perfect linear relationship). Increasingly negative correlation indicates an increasingly strong negative linear relationship (down to -1, which indicates a perfect inverse linear relationship). The correlati

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(The combination formula, or the binomial formula): For example, if you select two of the ten stocks you are analyzing, how many ways can you select the stocks? 10! / [(10 - 2)! x 2!] = 45. <span>An ordered listing is known as a permutation, and the formula that counts the number of permutations is known as the permutation formula. The number of ways that we can choose r objects from a total of n objects, where the order i

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Regarding counting, there can never be more combinations than permutations for the same problem, because permutations take into account all possible orderings of items, whereas combinations do not.

he ten stocks you are analyzing and invest $10,000 in one stock and $20,000 in another stock, how many ways can you select the stocks? Note that the order of your selection is important in this case. 10 P 2 = 10!/(10 - 2)! = 90 <span>Note that there can never be more combinations than permutations for the same problem, because permutations take into account all possible orderings of items, whereas combinations do not. <span><body><html>

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the covariance between two random variables is the probability-weighted average of the cross-products of each random variable’s deviation from its own expected value.

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l>In analyses of probabilities presented in tables, unconditional probabilities usually appear at the ends or margins of the table, hence the term marginal probability. Because of possible confusion with the way marginal is used in economics (roughly meaning incremental), we use the term unconditional probability throughout this discussion.<html>

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If we know both the set of all the distinct possible outcomes of a random variable and the assignment of probabilities to those outcomes—the probability distribution of the random variable—we have a complete description of the random variable, and we can assign a probability to any event that we might describe

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A mutual fund guide ranked 18 bond mutual funds by total returns for the year 2014. The guide also assigned each fund one of five risk labels: high risk (four funds), above-average risk (four funds), average risk (t

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