Mathematica 2014

8

So;

W ୅ W ୆

ൌ 14.14 7.07

And;

W B

= 2W A

Since W A + W B =1, then; ଵ ଷ And by plugging this into the equation for returns, we get; W A = ଶ ଷ & W B =

E(R P ଵ ଷ (25) = 15% So, if you have the exact securities A and B as above, and two thirds of your portfolio consists of A and the rest B, then you will get 15% return with 0% risk. Smashing. These equations will actually produce curves on a graph of return against risk, so investors can choose shares with certain levels of risk and return, with the variables being; S, E(R P ), and W A :W B , that they feel will maximise profit (whilst bearing in mind the relative risk associated with the investment). To conclude though, I must mention that the chances that past data will perfectly link to future market fluctuations and hence that the inductive reasoning in the calculations will give you the undisputed values for risk and return is almost as close to nil as you can get. Although a famous stock investor called John Templeton did once say “The four most dangerous words in investment are; ‘this time it’s different’”, suggesting market trends actually mean everything. However, many theories that have been formulated over the years in many different fields of academia have certain annoying parameters that are tricky to get round. Nevertheless, I feel that the underlying principle here that is really interesting is that if an investor can combine any number of securities and combine them in a portfolio, they can expect to get the weighted average of the returns with less than the weighted average of the risk (given the PMCC is less than 1 which reduces the value of the portfolio risk equation and hence brings the value of the standard deviation below that of the returns you get from the same assets). I also think it is worth mentioning that these ideas are not restricted to situations with only two assets. The general equation for return (or expectation in S1) is simple; you just add a summation sign (Σ) and set the limits between 1 and ‘n’ for the % return and portion of portfolio taken by asset ‘i’. The equation for risk is as follows; V ୔ ൌ ෍W ୧ ଶ S ୧ ଶ ୧ୀ୬ ୧ୀଵ ෍෍W ୧ W ୨ S ୧ S ୨ PMCC ୧୨ ୨ୀ୬ ୨ୀ୬ ୧ୀ୬ ୧ୀଵ I leave you with a quote from the late Phillip Fisher, an American stock investor, ) = ଶ ଷ (10) +

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