Financial Management

Financial Management

Question 1

Explain, with examples, how you would measure risk of a single asset

Definition

The general definition of the risk is as volatility, measured by standard deviation. However, it is not easy to define the concept of risk. It exists the future is uncertain, the investment result have probability to loss or have any changing. The estimated return will not be achieved.

Volatility which is equal to risk seems to be the common approach from trading. The smaller standard deviation, the tighter is probability distribution of the rate return. Therefore, the lower is the risk of the investment. The two parameters of the distribution are the expected return and the standard deviation.

Advantage & Disadvantage

The two aspects of risk is there a reward for bearing risk and the greater the potential reward, the greater is the risk.

However, all the past performance only a guide for future performance, thus, the risk & rewards is not guarantee.

Expected return

Definition

"Risk must be exists in an expected return, and the different from investment decision forecast must exists risk." (Eugene F. Brigham & Louis C. Gapenski, 1994) The expected value of an investment is simply the average of a set of values weighted according to the familiar of occurrence. The method of calculates may be used to find expected sales or the expected cost of breakdowns for a machine or even the expected net present value of a whole project. It is able to get all the outcomes or cash flows to be considered and incorporated into a final expected value.

Formula

The formula of expected return:

Expected Return = P1 x R1 + P2 x R2 +...Pn x Rn

Where

P1= Probability of investment 1

R1=Expect return from investment 1

Example

There are 3 states of the economy:

State Probability A&B C&D

RecessionNormalBoom 0.30.40.5 -10%15%30% -30%13%20%

A&B Expected return is =(0.3*-10%)+(0.4*15%)+(0.5*30%)= 18%

C&D Expected return is =(0.2*-30%)+(0.35x*13%)+(0.45*20%)=7.55%

Standard Deviation

Definition

Investors to measure the risk of a stock or a stock portfolio often use it. The standard deviation is a measure of volatility is the amount of swing in performance that an investment can be expected to have from year to year.

The standard deviation is an investment's average variation from the average return. The higher the standard deviation which the greater the volatility, greater the risk.

Formula

As another way, it can shows as:

s =е (R 1- E(R))І P1

Where

R 1=Expected return for each year of investment

P1=Probability of occurrence of Investment 1

Example

Economic Outcome Probability Return on Investment

Excellence 25% 25%

Good 35% 20%

Average 28% 10%

Worse 7% 0%

Economic Outcome Return on Investment ERR - the Expected Rate of Return squared Probability of the Economic Outcome

Excellence 25% - 12.5% = 12.5 156.25 X 25% = 39

Good 20% - 12.5% = 7.5 56.25 X 35% = 19.68

Average 10% - 12.5% = -2.5 6.25 X 28% = 1.75

Worse 0% - 12.5% = -12.5 156.25 X 7% = 10.93

Total = 71.36

Answer:

Total Variance is 71.36.

The square root of 71.36 = 8.45

So the Standard Deviation is 8.45

Explain, with examples, how you would measure risk of a portfolio

Definition

Investors must take account of the interplay between asset returns when evaluating the risk of a portfolio. At a most basic level, for example, "an insurance contract serves to reduce risk by providing a large payoff when another part of the portfolio is faring poorly." (Eugene F. Brigham & Louis C. Gapenski, 1994)

Reduce Risk

Another means to control portfolio risk is diversification, investments are made in a wide variety of assets that the exposure to the risk of any particular security is limited. It just same as putting one's eggs in many baskets, overall portfolio risk actually may be less than the risk of any component security considered in isolation.

Formula

Portfolio weight for investment A = Value of investment A

Total value of all investment

Formula of portfolio variance :

sP = е [(E(Rs) - E(RP))2 Ps]

Formula of portfolio standard deviation:

sP2 = е [(E(Rs) - E(RP))2 Ps]

Example

State Probability A&B Expected Return C&D Expected Return

RecessionNormalBoom 0.30.40.5 -10%15%30% -3%6%15% -30%13%20% -9%5.2%10%

18% 6.2%