Portfolio Analysis and Modern Portfolio Theory

Square of correlation coefficient

A portfolio is a collection of investment vehicles assembled to meet one or more investment goals. Primary objectives include growth-oriented, income-oriented, and capital preserving portfolios.

An efficient portfolio is one that provides the highest return for a given level of risk. Investors will choose the investment with the highest potential return for a given level of risk or the one with the least risk for a given return.

That a high percentage of the variability in the returns of one asset can be explained by the returns of the other asset

The main characteristics of any investment are investment return and risk. These are important because they help investors compare various alternatives of investments and make informed decisions.

Because it reduces overall risk in a portfolio more effectively than combining uncorrelated or positively correlated assets

The ultimate objective for any investor is to achieve a high rate of return. This is measured by the rate at which their funds have grown during the investment period.

It will not provide sufficient diversification

It offers more diverse investment alternatives and potentially greater returns and reduced portfolio risk

The expected rate of return and the variance or standard deviation provide investors with information about the nature of the probability distribution associated with a single asset.

It involves currency exchange and political risk, is less convenient to invest, and is more expensive due to transaction costs

The three primary objectives of a portfolio are growth-oriented, income-oriented, and capital preserving. Growth-oriented portfolios aim for long-term price appreciation, income-oriented portfolios aim for current dividend and interest income, and capital preserving portfolios aim to earn marginal income without depleting capital.

To deal with uncertain outcomes in investing

The key measure of an investor's success is the rate at which their funds have grown during the investment period. This is evaluated by measuring the rate of return on investment.

Because investing usually involves dealing with uncertain outcomes

Precise quantitative measures are necessary for comparing various alternatives of investments to make informed decisions.

To minimize the portfolio variance

By adding a little weight to the security with a lower covariance and subtracting a little from the security with a higher covariance, and repeating the process until the variance cannot be lowered anymore

All securities have the same covariance with the portfolio

Because it allows for the minimization of portfolio variance

To divide funds into different asset classes

A disciplined, personalized process

Covariances are used to find the minimum variance portfolio

The investment opportunity set looks different when there are many assets

cov(rapple, rapple) = var(rapple)

The covariance matrix is symmetric

E(rp) = wa.E(ra) + ws.E(rs) + wh.E(rh)

∂²(rp) = wa².∂²(ra) + ws² ∂²(rs) + w²h ∂²(rh) + 2waws cov(ra, rs) + 2wawh cov(ra, rh) + 2wswh cov(rs, rh)

rp = w1r1 + w2r2 + · · · + wnrn

The sum of the weights equals one

E(rp) = w1E(r1) + w2E(r2) + · · · + wnE(rn) = ∑wiE(ri)

∂²(rp) = w1².∂²(r1) + w2² ∂²(r2) +......+ w²n ∂²(rn) + 2w1w2 cov(r1, r2) + ...

The CAPM describes the relationship between the expected risk premium on a security, E(Ri)-Rf, and the risk, beta.

E(Ra) = Rf + ba[E(RM) – Rf]

The beta (ba) represents the risk of an asset or a portfolio.

15.18%

Holding a combination of two assets with different parameters can reduce risk and increase expected return.

You calculate the expected rate of return by multiplying each possible rate of return by its probability of occurrence and summing the products.

The purpose is to measure the risk or uncertainty of an investment.

The risk of the portfolio is reduced when you combine two assets with different parameters.