Q) Obtain daily, weekly and monthly closing prices of the stock given to you. Get adjusted closing prices. Daily and weekly prices should be for one financial year. Monthly prices should be for 2 years. E.g. FY 2011-2012 and FY 2010-11. Compute annualized return and risk.

OBSERVATION
As can be seen from the observations above, the stock which gives the maximum return also comes with the maximum risk (TATA STEEL). So when it comes to selecting the stock, the following two cases can be considered:

a) Maximum return :- If you are a person who values maximum return and is willing to take the risk for the same, go for TATA STEEL

b) Minimum Risk :- If you are a risk averse person, go for JSP as the risk associated with it is less compared to TATA STEEL

In either case, whether TATA STEEL or JSP, the annualized return is negative.

Q) Construct 10 different portfolios with another company (Correl < 0.70) and compute return and risk for each portfolio. Identify the best portfolio. Construct the minimum variance portfolio.

Company| Correl|
JSP AND TATA STEEL| 0.89|
JSP AND CUMMINS| 0.65|

Initially we compared JSP and TATA STEEL. We found the Correl = 0.89 which was greater than 0.70. Next we compared JSP and Cummins and found the Correl to be 0.65. So we will choose Cummins for making the portfolio.

...the context of a portfolio, the risk of an asset is divided into two parts: diversifiable risk (unsystematic risk) and market risk (systematic risk). Diversifiable risk arises from company-specific factors and hence can be washed away through diversification. Market risk stems from general market movements and hence cannot be diversified away. For a diversified investor what matters is the market risk and not the diversifiable risk. (4)In general, investors are risk-averse. So, they want to be compensated for bearing market risk. In a well-ordered market there is a linear relationship between market risk and expected return. (1) RISK AND RETURN OF A SINGLE ASSET: Capital gains/ loss yield Current Yield Rate of Return=[Annual income/Beginning price]+[{Ending price-Beginning price}/ Beginning price] OR Total return = Dividend + Capital gain=
Rate of return Dividend yield Capital gain yield R1 DIV1 P1 P DIV1 P P 0 0 1 P P P 0 0 0
(2) PROBABILITY DISTRIBUTION AND EXPECTED RATE OF RETURN: E(R)=∑(i=1 to n)=p(i) *R(i), where, E(R)=expected return, n=number of possible outcomes, p(i)=probability associated with R(i), R(i)=return for the ith possible outcome....

...Risk and Return
Assignment Questions
1. Suppose a stock begins the year with a price of $25 per share and ends with a price of $35 per share. During the year it paid a $2 dividend per share. What are its dividend yield, its capital gain, and its total return for the year?
2. An investor receives the following dollar returns a stock investment of $25:
$1.00 of dividends
Share price rise of $2.00
Calculate the investor’s total return.
3. Below are the probabilities for the economy’s five possible states next year, with the corresponding returns on the market and on Trebli, Inc., stock
Economic Condition
Probability
Market Return
Trebli Return
Rapid expansion
0.12
0.23
0.12
Moderate expansion
0.40
0.18
0.09
No growth
0.25
0.15
0.05
Moderate contraction
0.15
0.09
0.01
Serious contraction
0.08
0.03
-0.02
a. What is the expected return on the market?
b. What is the expected return on the Trebli stock?
4. Tabulated below are the returns from 1935 through 1939 on small-company stocks and on the large-company common stocks.
Year
Small Company Stocks (%)
Large Company Common Stocks (%)
1935
47.7
46.9
1936
33.9
32.4
1937
-35.0
-35.7
1938
31.0
32.3
1939
-0.5
-1.5
a. Calculate the average return for the small company stocks and large company common...

...themselves to risk. Your personality and lifestyle play a big role in how much risk you are comfortably able to take on. If you invest in stocks and have trouble sleeping at night, you are probably taking on too much risk. Risk is defined as the chance that an investment's actual return will be different than expected. This includes the possibility of losing some or all of the original investment.
A financial decision typically involves risk. For example, a company that borrows money faces the risk that interest rates may change, and a company that builds a new factory faces the risk that product sales may be lower than expected. These and many other decisions involve future cash flows that are risky. Investors generally dislike risk, but they are also unable to avoid it.
To make effective financial decisions, managers need to understand what causes risk, how it should be measured and the effect of risk on the rate of return required by investors. These issues are discussed in this chapter using the framework of portfolio theory, which shows how investors can maximize the expected return on a portfolio of risky assets for a given level of risk. The relationship between risk and expected return is first described by the capital asset pricing model...

...CHAPTER 22
estimating risk and
return on assets
1. WHAT IS RISK?
Risk is the variability of an asset’s future returns. When only one return is possible, there is no risk. When more than one return is possible, the asset is risky. The greater the variability, the greater the risk.
2. RISK – RETURN RELATIONSHIP
Investmentrisk is related to the probability of actually earning less than the expected return – the greater the chance of low or negative returns, the riskier the investment. Investors take on higher risk investments in expectation of earning higher returns. Of course taking risk also means that the investor does not guarantee that the investment will be recovered.
3. PROBABILITY AND PROBABILITY DISTRIBUTION
Probability – is the percentage chance that an event will occur. It range between 0 and 1.0.
Probability Distribution – If all possible events or outcomes are listed and the probability is assigned to each event, the listing is called a probability distribution. It may be :
An objective probability distribution is generally based on past outcomes of similar events while asubjective probability distribution is based on opinions or “educated guesses” about the likelihood that an event will have a...

...a. What are investment returns? What is the return on an investment that costs $1,000 and is sold after 1 year for $1,100?
Investment returns is the expectation of earning money in the future on the amount of money invested. The return is the financial performance of the investment. The return is the difference between the amount invested and the amount you are returned after said investment.
There are two ways to show return on investment.
1. By dollar return.
Amount to be received – Amount invested
= $1,100 - $1,000 = $100 in return
The problems with expressing returns in dollars, you don’t know the size of the investment for that dollar return and you don’t know the timing of the return.
2. Rate of Return or percentage returns
Amount received – Amount invested / Amount invested
= $100 / $1000 = .10 = 10%
The rate of return “standardizes” the dollar return by considering the timing
b. (1) Why is the T-bill’s return independent of the state of the economy? Do T-bill’s promise a completely risk-free return? (2)Why are Alta Industries’s returns expected to move with the economy whereas Repo Men’s are expected to move counter to the economy?
(1) The...

...RISK & RETURN
TOPIC 4
Learning Objectives
1. Understand the meaning of risk and return
2. Identify risk and return relationship
3. Discuss the measurement of expected return
and standard deviation
4. Understand portfolio and diversification
5. Distinguish the different types of investment
risks
6. Measurement of return based on CAPM
WRMAS
2RETURN DEFINED
• Return represents the total gain or loss on an investment.
•
Basic concept:
Each investor desires a return for every single dollar of their
investment.
Example 1:
Rita invests in 10 unit shares valued at RM1000. At the end of
year, she sells all the shares @ RM1100. How much return
received by Rita for her investment?
RM100 (Holding return dollar gain)
r = RM1,100 + 0 – RM1,000
RM1,000
= 10% (so holding period rate of return is 10%)
WRMAS
3
Return Defined
Exercise 1
Calculate the holding period rate of return of each
quarter below.
1st Quarter
2nd Quarter
3rd Quarter
4th Quarter
Dividend
0.50
1.20
0
1.95
Purchase price
100
98
101
102
Selling Price
98
101
102
108
HP Rate of
Return
?
?
?
?
WRMAS
4
EXPECTED RETURN
• Expected...

...expected return on a risky asset.
c. the expected return on a collection of risky assets.
d. the variance of returns for a risky asset.
e. the standard deviation of returns for a collection of risky assets.
PORTFOLIO WEIGHTS
2. The percentage of a portfolio’s total value invested in a particular asset is called that asset’s:
a. portfolio return.
b. portfolio weight.
c. portfoliorisk.
d. rate of return.
e. investment value.
SYSTEMATIC RISK
3. Risk that affects a large number of assets, each to a greater or lesser degree, is called _____ risk.
a. idiosyncratic
b. diversifiable
c. systematic
d. asset-specific
e. total
UNSYSTEMATIC RISK
4. Risk that affects at most a small number of assets is called _____ risk.
a. portfolio
b. undiversifiable
c. market
d. unsystematic
e. total
PRINCIPLE OF DIVERSIFICATION
5. The principle of diversification tells us that:
a. concentrating an investment in two or three large stocks will eliminate all of your risk.
b. concentrating an investment in three companies all within the same industry will greatly reduce your overall risk.
c. spreading an investment across five diverse companies will not lower your...

...1. Convert prices to total return (% change in the price) = (Pt – Pt-1) / Pt-1
2. Remove outliers – sort data and remove anything +/- 20%
3. Calculate historical average and historical risk
X-BAR = Σx/n
Calculate the sum of the total return and divide by the number of observations
• Variance = σ2 = Σ(x – x bar) 2 / (n-1)
Fix X-BAR, double click to apply to all dates, get the sum, divide by (n-1)
Risk = σ = √σ = SQRT(Variance) = standard deviation
4. Average Matrix
Excel Options → Add-ins → Go → Select 1st two and last one → Go
Data Analysis → Descriptive Analysis → Select all data without the time → Label in the first row → Select “Summary Statistics” → OK
• This gives you the averages: average matrix
[ xbar, xbar2, xbar3, ….]
5. Covariance Matrix
Data analysis → Covariance → OK → Select all stocks like before → Labels in the 1st row → OK
• This gives you the covariance matrix
• To fill out the matrix: Copy → Paste Special → Transpose
•
6. Generating Scenarios
Data Analysis → Random number generation → # of variables: 6 (the number of companies in the portfolio) → # of random numbers: 10 000 → distribution: uniform
Calculate the sum of each row for the weights, they’ll never = 1
Normalize the weights: divide the weight of each stock by the sum of all the weights; this makes the weights=1
• You cannot fix the sums. So, copy/paste the sums 3 times if you have 3 weights,...