Question

(a) It is commonly accepted that there are gains from adding securities to an
investment portfolio. Explain what is meant by this statement. (Your answer
should include a discussion and example regarding systematic and
non‐systematic risk as well as an indication of the optimal number of assets to be
included within a portfolio in theory and in practice.)

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(b) The following table provides monthly percentage price changes for two well
known market indexes.

Month Russell
2000

Nikkei
1 0.04 0.04
2 0.10 ‐0.02
3 ‐0.04 0.07
4 0.03 0.02
5 0.11 0.02
6 ‐0.08 0.06

Answer the following:
(i) What have you assumed about the distribution of data (that is,
have you assumed the data is a sample or a population).

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(ii) Calculate the expected monthly rate of return and standard deviation for
each market index. (Hint: Use your calculator as no marks will be
provided for working in this particular question.)

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(iii) Calculate the correlation coefficient for Russell 2000 – Nikkei. (Hint: Use
your calculator as no marks will be provided for working in this particular
question.)

Answer 1

a)

It is commonly accepted that there are gains from adding securities to an
investment portfolio.

When we add securities to a portfolio, it is observed that the risk of the overall portfolio as measured by standard deviation of the returns reduces. This improves the risk adjusted return and hence one can say that there are gains in adding securities to a portfolio as the increased return exceeds the cost in terms of inreased standard deviation.

Let us consider a single security which we own. If we add a riskier security to this asset to make our portfolio in equal proportion, i.e the weights of each asset in the portfolio is 50%. The return measured by the weighted average would be right in the middle of he individual returns of the asset.But when we go to calculate the standard deviation of the two assets, there is a correlation term,rho. The rho will be 1 only if the asset have perfectly correlated returns. That is generally never the case and rho turns out to be less than 1. This makes the standard deviation mathematically lesser than the simple average and hence reduces the overall standard deviation and the risk. Higher return for lower costs(lower risk) is a gain.

We have to understand that the portfolio will have two major sources of risk, systematic risk which is out of the control of the asset and is due to the externalities and market. This risk is known as non diversifiable risk. This risk is due to the larger industry and market happenings and is being faced largely by all assets.

The other major risk is unsystematic risk or company specific risk. This risk is also known as diversifiable risk as the risk is caused due to the interplay of the asset's structure, mechanics with the other surrounding factors. These are risks commonly associated with company specfic events. When we cannot predict wth accuracy over the nature of the change(positive or negative) to the asset, we can diversify our portfolio by adding assets which have different prevailing conditions to our original asset. This can be determined from correlation of returns bertween the two assets. When there isn't much correlation between the two assets, we have diversified our losses.

But as we agree to the idea that diversification generally gives one good gains, we have to take notice of the exceses of diversification and not go about adding assets to our portfolio. The main opposition to uninhibited diversification is that there are costs in managing the portfolio and in practice, beyond a certain number of assets, the investor wll find it strenous to keep track of the securities in the portfolio. The Markowitz theory of portfolio allocation has assumptions of no transaction costs and efficient capital markets which seldom is the case. Hence, there is a limit, an optimum number of assets to be included in the potfolio under the constraints of variable transaction costs and inefficient capital markets.