10. Concept of Time Value of Money helps in arriving at comparable value of different rupee amounts at different points of time into equivalent values of particular time.
12. For TVM analysis, it is better to draw time line first denoting at what time how much cash flows have occurred
13.
14.
15.
16.
17. 0 1 2 3 Annuities An annuity due is a finite set of sequential cash flows, all with the same value A, which has a first cash flow that is paid immediately. Ordinary Annuity Timeline i% A A A 10
18. Ordinary Annuity 0 1 2 3 i% PMT PMT PMT Annuity Due 0 1 2 3 i% PMT PMT PMT PV FV Ordinary Annuity vs. Annuity Due 11
22. How much value is created from undertaking an investment?
23. The first step is to estimate the expected future cash flows
24. The second step is to estimate the required return for projects of this risk level.
25. The third step is to find the present value of the cash flows
26.
27. A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.
28.
29. It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere
30. It is the interest rate at which PV of cash flows equates with PV cash outflows. Alternatively, at IRR, NPV of the project is zero.
31.
32. IRR can be misleading when mutually exclusively projects are compared as this method assumes that cash flows are reinvested at IRR only which may not be possible in every situation
33.
34. Holding period return is independent of the passage of time.When comparing investments, the periods should all be of the same length. Ending Beginning value value Income _ Holding period = return + Beginning value
37. It is the rate at which Re.1 is compounded over a specified period of time
38.
39. Money weighted Return The Money-Weighted Rate of Return (MWRR)…same as internal rate of return of portfolio. Initial deposit is considered as inflows and all withdrawals and ending value is considered as outflows. Not good for comparing different fund managers as MWRR over 0-T is also, generally, a function of the amount and timing of net new money – which is not in the control of the fund manager.
64. In such cases the usual mean is not good representative of data. Therefore we are obtaining weighted mean by assigning weights to each item according to their importance.
65. WM = sum(wx) sum(w)
66.
67. It divides whole data into equal portion. In other words 50% observations will be smaller than the median and 50% will be larger than it.
103. Skewness occurs because the arithmetic mean of the population is not equal to its median since the mean is influenced by some extreme outliers
104. Degree of skewness of a distribution can be measured using the coefficient of skewness, Sk
105. If Sk is positive the distribution is positively skewed
106.
107. Usually: mode < median < meanExample: Gamblers tend to like returns that are positively skewed because of the likelihood (however small) of a very large return
108. Negative Skewed Distribution Negative: tails to the left Usually: mean < median < mode Example Typically investors would not prefer negatively skewed instruments since it means that there is a likelihood (however small) of a very large loss
109.
110. Kurtosis is an important consideration in risk management
128. Probability of an event regardless of the past/future occurrence of other events. Ex. Probability of Economic recession without considering probability of change sin interest rate and inflation
133. Dependent Events : If the above two conditions are not satisfied , events are dependent eventsExample: Economic recession and decrease in interest rates are dependent events.
136. Forecasts are made using the expected value for a stock’s return, earning etc.
137.
138. A negative covariance between X and Y means that when X is above its mean its is likely that Y is below its mean value.
139. If the covariance of the two random variables is zero then on average the values of the two variables are unrelated.Cov( Ri, Rj) = E { [Ri– E(Ri) ] [Rj– E(Rj) ] }
142. A correlation of 0 means there is no straight-line (linear) relationship between the two variables.
143. Increasingly positive (negative) correlations indicate an increasingly strong positive (negative) linear relationship between the variables.
144. When the correlation equals 1 (-1) there is a perfect positive (negative) linear relationship between the two variables.Corr ( Ri, Rj) = [ Cov ( Ri, Rj) ] / [(Ri) (Rj) ]
149. P(R) is the probability that a fruit is red and round (prior probability), regardless of whether it is an apple or not
150. P(A) is the probability that a fruit is an apple (prior probability) regardless of whether or not it is round and red
151. Bayes theorem allows us to infer the posterior probability P(A|R) if we know P(A), P(R) and P(R|A)
152. P(A|R) = [P(R|A)*P(A)]/P(R) Updated probability = Varied applications in business decision making including evaluation of mutual fund performance
153.
154. Only one item to be selected from each group and two or more groups are present. Use multiplication rule.
155. When n items are to be arranged and none of them belong to any group. Use ‘n’ Factorial.
156. Each element of entire group must be a assigned a place, label in one of the three or more sub groups of predetermined size. Use the labeling formula.
157. When one needs to choose or select from two groups of predetermines size. Use Combination formula
173. Continuous Random Variable :The number of possible outcomes are infinite even within a range of values P(x) = 0 , even when x can occur. We can define probability P(x1 <= X <= X2 )
205. Total area under curve = 1Also Note: area within + or - 2 standard deviations is 95.4% 2) Area within + or - 1 standard deviation is 68.3% 99.7% Wide ranging applications in Modern Portfolio Theory and Risk Management
206.
207.
208. Hence they allow us to draw more meaningful conclusions on top of a point estimate
209. A Confidence intervals is a interval for which we can say with a certain level of probability, called the degree of confidence, that it will contain the parameter intended to estimate.
232. It is based on the repeated generation of one or more risk factors that affect security values, in order to generate distribution of security values
233. Random values of Risk factors are generated using the computer based on the parameters of the probability distribution these risk factors follow
237. It is based on actual changes in risk factors over some period of time
238. Simulation involves randomly selecting one of the past changes in risk factors and then calculating the value of security/ asset based on the changes in risk factors
270. As the degrees of freedom (sample size) gets larger, the shape of the t-distribution more closely approaches a standard normal distribution.
271. When compare to the normal distribution, the t-distribution is flatter with more area under the tails, as the degrees of freedom, df, for the t-distribution increases, its shape approaches that of the normal distribution.
285. Given a sample (post event) we can define confidence intervals to state our expectation that a population parameter falls within a certain range given the observations of the sample
301. Note: The first example above calls for a two tailed test, i.e. null is rejected if the data suggests that the mean return is either smaller than 6% or larger than 6%
302.
303. Our decision on accepting or rejecting the hypothesis would be based on a comparison between the calculated test statistic and a specified set of possible values; these values are primarily a factor of the level of significance
304. There are 4 possible outcomes from a hypothesis test:
326. The test statistic then becomes [X(bar) - ]/S(xbar)Sample statistic – Value of population parameter under H(0) Test statistic = Standard error of the sample statistic
327.
328. It is also an alternate way of hypothesis testing
329. Compare p value of the hypothesis test with the level of significance of the test
330. If the p value is larger than the level of significance the null hypothesis is accepted
331. If it is smaller than the level of significance the null hypotheses is not accepted
332. The p test gives the same result as the t test but it provides additional information that makes it more powerful
333.
334. t test: used for testing arithmetic means of populations;
346. Assumes that the population variances are equal (although unknown); samples are independent
347. If we are not able to assume the population variance are equal then we have an approximate t test
348. The null hypothesis may be formulated as (1 - 2) = 0 (or <=0 or >=0)With appropriate alternative hypothesis
349.
350. Test concerning mean diffrences For data consisting of paired observations from samples generated by normally distributed populations with unknown variance the t-test is as follows: Applications include: Test whether the mean returns earned by two investment strategies were equal over a particular period of time In this case the since both strategies are likely to have common risk factors such as market return the samples are dependent; hence we need to apply this test since by calculating the standard error based on differences we are accounting for correlation between the observations Pairs of before and after observations such as dividend returns before and after a change in tax laws t = [d(bar) – (d0)]/sd(bar) With n-1 degrees of freedom and Sd(bar) = sd/(n)^(1/2) Sample variance Sd^2 = {∑[(di – dbar)^2]}/(n-1) Sample mean difference, dbar=(1/n) ∑di
355. If sample is not random or underlying population is not normal then inferences can be wrongTest statistic, X^2 = [(n-1)(s^2)]/(0^2) With n-1 degrees of freedom and S^2 = {∑[(xi – xbar)^2]}/(n-1)
356.
357. For two samples the first with n1 observations and sample variance s1^2 and the second with n2 observations and sample variance of s2^2
364. Hence the rejection point for any formulation of hypothesis (for this distribution and convention) is a single value in the right hand side of the relevant F distribution
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