Portfolio analysis
it considers the determination of future risk and return while holding various blends of individual securities and assets
If
... [Show More] corporate returns exceeds market's expectations, share price should _______________.
rise
Efficient portfolio
one which minimises risk without impairing return, or maximize the return for given level of risk
Portfolio theory provides _______________ to investors to make decisions to invest their wealth in assets or securities under risk.
normative approach
One important conclusion of the portfolio theory is
if the investors hold a well-diversified
portfolio of assets, then their concern should be the
expected rate of return and risk of the portfolio rather
than individual assets and the contribution of individual
asset to the portfolio risk.
Assumptions of portfolio theory
Investors are risk-averse and rational being; the returns of assets are normally distributed.
Foundations of portfolio decisions
mean (the expected value) and variance (or standard deviation) analysis
What is CAPM?
We can extend the portfolio theory to derive a framework for valuing risky assets. This framework is referred to as the capital asset pricing model (CAPM).
What is APT?
An alternative model for valuation of risky asset is Arbitrage Pricing Theory.
PORTFOLIO RETURN
It is equal to the weighted average of the returns of individual assets (or securities) in the portfolio with weights being equal to the proportion of investment value in each asset.
Given the expected returns of individual assets, the
portfolio return depends on
the weights (investment
proportions) of assets.
Formula for portfolio return
In term of weight and probability
Positive covariance
Returns are above or below at the same time.
Negative covariance
Two returns are at opposite ends of the average returns
What Is Co-variance?
Co-variance measures the directional relationship between the returns on two assets. A positive co-variance means that asset returns move together while a negative co-variance means they move inversely.
Relation between Covariance and Correlation
Covariance X, Y = SD, X SD, Y Correlation XY
Individual assets are more risky than the portfolio. True or False
True. Returns on
individual assets fluctuate more than the portfolio return.
The portfolio variance or standard deviation depends
on the co-movement of returns on two assets.
Value of Correlation
minus one to plus one
Variance of two-asset IS NOT weighted average of the variance of asset. Why
because they covary as well
Variance of portfolio
includes proportionate variance of individual securities and covariance of securities.
Covariance depends upon
correlation between the securities in the portfolio
What Is a Minimum Variance Portfolio?
A minimum variance portfolio is a collection of securities that combine to minimize the price volatility of the overall portfolio. Volatility is a statistical measure of a particular security's price movement (ups and downs).
Optimum portfolio
The minimum variance portfolio is also called the optimum portfolio.
When diversification reduces the risk?
diversification always reduces risk provided the correlation coefficient is less than 1.
Why is that a perfect negative correlation will not generally
be found in practice?
Securities do have a tendency of moving together to some extent, and therefore, risk may not be totally eliminated.
Special situation in Portfolio risk return analysis
Perfectly positive correlation, Perfectly negative correlation and zero correlation
Why is perfectly positive correlation not preferred?
There is no advantage of diversification when the returns of securities have perfect positive correlation.
Why is perfectly negative correlation preferred?
In this the portfolio return increases and the portfolio risk declines. It results in risk-less portfolio.
Zero Correlation
means returns from two securities are independent of each other.
The proportions of securities in the portfolio that would
result in zero-standard deviation portfolio
w'x = sigma y divided by (sigma x + sigma y)
Investment Opportunity Set
The investment or portfolio opportunity set represents all possible combinations of risk and return resulting from portfolios formed by varying proportions of individual securities.
It presents the investor with the risk-return trade-off. What is it?
Investment Opportunity Set
Inefficient portfolios
have lower return and higher risk
An efficient portfolio
An efficient portfolio is one that has the highest expected returns for a given level of risk.
efficient frontier
the frontier formed by the set of efficient portfolios
inefficient portfolios
All other portfolios, which lie outside the efficient frontier
limits of diversification
When there are just two securities, there are equal
numbers of variance boxes and of covariance boxes. When there are many securities, the number of covariances is much larger than the number of variances. Thus the variability of a well-diversified portfolio reflects mainly the covariances.
PORTFOLIO RISK: THE n-ASSET CASE
Suppose we are dealing with portfolios in which equal investments are made in each of N stocks. The proportion invested in each stock is, therefore, 1/ N. So in each variance box we have (1/ N ) ^2 times the variance, and in each covariance box we have (1/ N )^2 times the covariance. There are N variance boxes and
N ^2 - N covariance boxes.
The variance of the portfolio is the weighted sum of average variance
and the average covariance of securities.
Portfolio variance = N * (1/N)^2
(average variance) + (N^2-N) (1/N)^2*
(average covariance)
When n approaches infinity (n → ∞),
the weight of the average variance becomes zero and the weight of the average covariance term becomes 1.
True or False: Portfolio variance (when n → ∞) = average covariance
True
True or False: The variance of securities diminishes as the number of securities increases
True
True or False: When more and more securities are included in a portfolio, the risk of individual securities in the portfolio is increased.
False
Systematic risk
arises on account of the economy-wide uncertainties and the tendency of individual securities to move together with changes in the market. AKA market risk and uncontrollable risk
Unsystematic risk
arises from the unique uncertainties of individual securities. AKA Unique risk
Key factors for systematic and unsystematic risk are
Systematic->external and macro-economic factors
Unsystematic->internal and micro-economic factors
Protection from unsystematic risk
Portfolio diversification
Protection from systematic risk
Asset allocation
Range of affect of systematic risk
Large number of securities in the market.
Range of affect of unsystematic risk
Only particular company.
Examples of systematic risks
the changes in government policy, the act of nature such as natural disaster, changes in the nation's economy, international economic components
Three category of systematic risk
Interest risk, Inflation risk and Market risk
Interest risk
Risk caused by the fluctuation in the rate or interest from time to time and affects interest-bearing securities like bonds and debentures.
Inflation risk
Alternatively known as purchasing power risk as it adversely affects the purchasing power of an individual. Such risk arises due to a rise in the cost of production, the rise in wages, etc.
Two categories of unsystematic risk
Business risk and financial risk
Business risk
The chance that the firm will be unable to cover its operating costs
financial risk
The chance that the firm will be unable to cover its financial obligations
examples of unsystematic risk
labor strikes, part shortages, expert resignation, loses contract, competitor enter market,
Is Total risk not relevant for an investor who holds
a diversified portfolio?
Yes. Total risk of a security = Unsystematic risk + Systematic risk. And systematic risk is only the thing of concern for investor.
How many securities should be held by an
investor to eliminate unsystematic risk?
In USA, it has been found that holding about fifteen shares can eliminate unsystematic risk.7 In the Indian context, a portfolio of 40 shares can almost totally eliminate unsystematic risk.
A risk-free asset or security
It has a zero variance or
standard deviation. The risk-free security has no risk
of default. [Show Less]