Mathematica 2014

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A-Level Statistics in Investment Banking and Portfolio Theory By Charlie Sparkes Investment banking is often made out to be like an impossible, unpredictable science that only those audacious enough to wear pin striped suits can ever fathom. However, as you may know, a crucial part of an investment banker’s day to day regime requires a lot of pondering over the magical relationship between risk and return and how to optimize the performance of a portfolio based on past and predicted data. Or, in S1 terms, this is the relationship between expected return (E(R) - return), standard deviation (S - risk) and the correlation coefficients (PMCC – just a coefficient in an equation). So, as this is a Maths essay, here is the inevitable set of data around which my explanations will revolve 1 . % Return Probability Security A Security B 0.25 20 45 0.50 10 25 0.25 0 5 Total = 1.00 Total = 30 Total = 75 S A = 7.07% S B = 14.14% Notation: R = % return, W A + W B = weight of portfolio invested in respective securities = 1 (in total), P = % return on portfolio of A and B. To calculate (a rather generalized) return on investments, using the data we can derive that; E(R P ) = W A E(R A ) + W B E(R B ) – i.e the weighted average return on A and B. So if the investor split his or her investment equally in A and B then, using the data; E(R P ) = 0.5(10) + 0.5(25) = 17.5% expected return on investment in the portfolio. Although I may have made some sweeping assumptions here, portfolio theory (and the law of large numbers) does suggest that for some overcompensating discrepancies that have been made, there will be some other discrepancies to counter these externalities, so the calculated expected returns value isn’t far off E(R A ) = 10% E(R B ) = 25% Var(R A ) = 50% Var(R B ) = 200%

1 An Introduction To The Stock Exchange – Janette Rutterford

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