# Archive for October 18th, 2012

### Investments, Risk and Return

Posted by Awais Ahmad in ACADEMIC on October 18, 2012

*Author: Awais Ahmad (comsian027@gmail.com)*

**Investment:**

Investment may be defined as an activity that commits funds in any financial/physical form in the present with an expectation of receiving additional return in the future. The expectation brings with it a probability that the quantum of return may vary from a minimum to maximum. This possibility of variation in the actual return is known as *Investment Risk*. Thus every investment involves a *Return* and *Risk*.

Investment is an activity that is undertaken by those who have *Savings*. *Savings* can be defined as the excess of Income over Expenditure. Two important characteristics of Investment are *Return* and *Risk*.

*Return:*

Every Investment has and expectation of Return, which is the margin earned by investor in future by investing at present. The margin earned reflects the concept of *Time Value of Money*, which describes that a Dollar currently held will be less worth tomorrow. Investors take advantage from this saving, which is called Return (denoted by ** k**or

**)**

*r**Risk:*

Risk is the chance of uncertainty that may rise after investment. It is the event that may arise by affecting the Return of the Investment. Every investor should forecast the Return and Risk while investing and should keep into account all possible events that may occur in future. It is denoted by ** d** and is the

*Standard Deviation*, which reflects the deviation from the

*Expected Rate of Return*.

The formulae for Risk and Return of and Investments are:

*Relationship between Risk and Return:*

Risk and Return have positive relation to each other (Direct Relationship):

Risk **µ** Return

The relationship shows that if an investment is tied with high expectation of Return, it will have high Risk and vice versa. This relationship is also shown in the diagram:

**Types of Risk:**

There are various types of Risk, among which, following are the most important to describe:

**1.****Business Risk:**

Business Risk is one which is tied to a particular business. Such risk arises when the investor is not sure whether the business will successful or not in which he/she has invested.

**2.****Financial Risk:**

Financial Risk is the additional risk placed on the common stockholders as a result of the decisions to finance with debt. The use of debt, also called *Financial Leverage* also concentrates the firm’s business risk on its stockholders. Financial Risk arises, when to decide whether the firm should be *Levered* (50% debt and a portion of equity) or *Unlevered* (All Equity). In this way, it makes the *Capital Structure* of a firm.

**3.****Country Risk:**

Country Risk is one that arises from a particular country. A country’s environment may be favourable for investors, who want to invest in that country. Investors need to forecast such risk before making the investment decision.

**4.****Diversifiable Risk/Unsystematic/Idiosyncratic:**

The part of a stock’s risk, that can be minimized/neglected is called Diversifiable Risk. Such Risk is caused by some random events like lawsuits, strikes, successful and unsuccessful marketing programs etc. This type of risk can be minimized while investing in multiple stocks; a phenomenon known as *Diversification Principle*.

**5.****Non-diversifiable/Systematic/Market Risk:**

The part of stock’s risk, that cannot be minimized or neglected is known as Non-diversifiable Risk. This type of risk stems from factors that systematically affect most firms; such as war, inflation, recessions and high interest rates. Such risk remains constant even when investing in multiple stocks. It is measured in terms of Beta (β).

**6.****Inflation Risk:**

Technically speaking, this type of risk is a subtype of Systematic Risk. This risk stems from variation in inflation rate. When inflation rate increases, it reduces the *Real Interest Rate* and vice versa. More detail about the relationship between Inflation Rate and Real Interest Rate will be explained in related articles.

**7.****Interest Rate Risk:**

Interest Rate Risk can be said to be a subtype of Systematic Risk. This type of risk arises with the fluctuation on Interest Rate in market. The more is the market Interest Rate, the more will be Interest Rate Risk tied to a particular stock (will be explained in later articles).

**8.****Exchange Rate Risk:**

Exchange Rate Risk stems from changes in Exchange Rate or currency fluctuations. The more is the currency fluctuation in market, the more will be the Exchange Rate Risk for and Investor.

**9.****Liquidity/Marketability Risk:**

Liquidity Risks generally arise when one business acquires another business. *Liquidity* refers to a condition when a firm is not generating enough profit from its operations, that can meet the overall cost of a business. By doing so, investors of one organization purchase the stocks of *Liquidating Firm*, but are not sure whether their decision to purchase the stocks of such firm will benefit at a future date or not. Such uncertain factors are called Liquidity Risk, when combine together.

**10.****Political Risk:**

Political Risk arise from the political environment of an economy. If a country’s political environment is uncertain and unfavourable, the investors are called facing Political Risk while investing in such country.

**11.****Stand-alone Risk:**

If an investor has only one investment, the risk tied to that particular investment is known as Stand-alone Risk. If an investor has only one investment, it is highly risky for him/her, as he/she cannot compensate his/her loss from alternative stocks, in case the stock hald by him/her is losing its value.

**12.****Portfolio Risk:**

If an investor has invested in multiple stocks/securities, the risk tied to all of those stocks/securities (combined together) is called Portfolio Risk. If a security defaults, the investor still has a chance to earn profit from other stocks/securities held by him/her. Portfolio Risk can be measured by the following formula.

*References:*

Investment Analysis and Portfolio Management (handouts)

Lectures by Mr. Wasim Anwar

Financial Management – Theory & Practice; 10e by *Eugene F. Brigham & Michael C. Ehrhardt*

### PROBABILITY OF A FAIR COIN (Experimental Proof)

Posted by Awais Ahmad in ACADEMIC on October 18, 2012

*Author: Awais Ahmad (comsian027@gmail.com)*

**PROVING THE PROBIBILITY OF A FAIR COIN TO BE 0.5 OR 50%**

Question: Prove with experiment that the Probability of a fair coin is 0.5 or 50%.

Experiment:

**Step 1:** Take a fair coin and toss it 200 times and record each observation and the outcomes thereof. The following observations were recorded by tossing a fair coin 200 times:

For the time being, for our convenience, we have classified the observations of the experiment with a difference of 25.

Here:

Head of the Fair Coin = N

Tail of the Fair Coin = M

As we see as per Table, First column shows the number of observations taken from the experiment, classified with the difference of 25. Second column shows the appearance of Head (N) or Tail (M) during the experiment.

**Step 2:** Now we perform calculations of Probability in further details by the table given below:

Colum 1 of Table shows the Number of Experiments’ Lower and Upper Limits (The data of 200 observations is classified with a difference of 5 for detailed analysis). Second column shows outcomes of appearing Head (N) or Tail (M), and Cumulative Outcomes. TOTAL Colum shows the number of experiments during a particular time. Next column shows the probabilities of appearing N or M of the coin and their Cumulative Probabilities. These probabilities are calculated by the following formula:

P (N) = N / (TOTAL)

P (M) = M / (TOTAL)

**Step 3:** Then P (N) and P (M) showed the cumulative probabilities of N and M respectively. The point should be noted that, before experiment performed, the Probabilities of both N and M were Zero. Last column shows the number of Cumulative Observations/Outcomes of the experiment. Last Row TOTAL showed that the experiment was repeated for 200 times, among which 98 times, N appeared and M appeared for 102 times.

Now we plot these values on the line graph, and can show the probabilities of N, M and both N & M on the same plot area.

**Conclusion:**

From the experiment Data and Graphical Representations, we can see that the Probabilities of Head (N) and Tail (M) are about equal to 0.5 (50%) when we repeat the same experiment for 200 times. So it is proved that the **Probability of a fair coin is 0.5 (50%).**

**Note:** If the same experiment is provided for more than 200 times, we can get more accurate results.

**References:**

Question from Statistics for Business and Economics – by David R. Anderson (Author), Dennis J. Sweeney (Author), Thomas A. Williams (Author), Jeffrey D. Camm (Author), James James J. Cochran (Author)

Experiment on Fair Coin