Introduction to finance and quantitative methods
- Ways of classifying financial markets
Financial markets refer to markets where exchanges of financial instruments take place. Financial markets can be categorized in the following ways:
- Nature of the products: Financial markets can be classified based on products ownership, the duration it takes to mature, how it is traded, size and how it can be transferred. Examples of such financial markets are equity and derivatives.
- Market participants: Market participants may be made up of professionals, non-professionals or officials of an institution. Under this criterion, financial markets can be classified as commercial banks, Central banks and non-financial institutions.
- Origin: Goods and services under this criterion traded locally, internationally or regionally. Examples of markets under this category are national markets and regional integrated markets
- Ways of trading: Trading can be carried out either physically, electronically or virtually. Markets under this criterion are over-the counter markets and internet.
b) Perpetuity is a project which exhibits constant cash flows which normally repeats for unlimited amount of time.
c) An asset is said to be positively correlated if the returns on different assets held by an investor move in same direction. On the other hand, negatively correlated assets are those whose returns move in opposite directions.
2. Annual growth rate of dividends is given by:
Where Dn is the dividend paid at the end of the period (2009), D0 is the amount paid at the beginning of the period (2002) and n is the number of years between the two periods.
Dividend growth rate = 81.841.15 - 1
= 81.6 – 1
= 1.0605 – 1
3. Amount is given by the formula
A = P [ 1+r]n
50,000= 3,000[ 1+0.06]n
1.06n = 16.67
Introducing logs on both sides
n =48 years
If r = 10%:
A = P [ 1+r]n
50,000= 3000 [ 1+0.1]n
4. PV= FV[1+r]n
Where PV=Present value
6. Amount at the end of first year=2000(1.05) = £2,100
Amount at the beginning of second year
Amount at the end of second year
Amount at the beginning of third year
= £3,255 + £2000
Amount at the end of third year
7. Price of a bond with a zero coupon = F0× PVIF
Where F0 is the face/par value while PVIF is present value interest factor
r = 7.52 = 0.0375
n = 50 × 2 = 100
PB = 1,000 × (1+0.0375)100
= 1,000 × 0.02519
8. Price of a bond with a coupon interest = Ci × PVIFA + F0 × PVIF
Where Ci is the coupon interest, PVIFA is the present value interest factor of an annuity, F0 is the face value and PVIF is present value interest factor.
Ci = 802 = 40
n = 20 × 2 = 40
r = 62 = 0.03
PB = 40 × 1-(1+0.03)-400.03 + 1,000 × (1+0.03)-40
= [40 × 23.11] + [1,000 × 0.3066]
= 924.4 + 306.6
- a) Diversification refers to ways by which investors reduces exposure to risk by holding a variety of assets to minimize overall risk of the portfolio one has invested in.
Benefits of diversification
Diversification enables an investor to minimize risk he or she is exposed to in holding a portfolio (Meyer 131). The reduction in the level of risks encountered has resulted to increase in earning by the investors since they are guaranteed of stable earnings. Diversification also boosts performances of firms as firms are able to earn positive gain from one market when the other is experiencing loses.
- Unsystematic risk is part of the total risk that is specific to an investment and can be eliminated by holding investments in a wide range of asset portfolios. Systematic risk on the other hand is not diversifiable and must be accepted by any investor who chooses to hold the asset.
- An asset is said to be positively correlated if return on different assets held by an investor move in same direction. On the other hand, negative correlation involves returns moving in opposite directions.
- Beta assumes that investors do not incur cost in transacting business and also they do not pay taxes. This is usually not as those who invest in stock are usually placed in different tax bracket. It also assumes that only a limited amount of stock can be traded and the rate of interest is fixed. There is also assumption of homogeneous expectations which require all investing in stock to have similar expectations and should analyze stock the same way.
- Rr = Rf + βt (Rm-Rf)
Rt = Required return
Rf n =Risk free rate of return
Rm = Return from the market
Β = Beta factor
18 = Rf +1.4(14-Rf)
Rf = 1.60.4
Rf = 4%
- a) Expected returns:
Expected return on A
= (0.35X0.04) + (0.5x0.04) + (0.15x0.04)
Expected return on B
= 90.35X0.210) + (0.5X0.08) + (0.15X-0.01)
Expected return on C
= (0.35X0.300) + (0.50x0.200) + (0.015X0.26)
Variance of asset A
= [(0.04-0.04)2x0.35] + [(0.04-0.04)2x0.50] + [(0.04-0.04)2x0.15]
Variance of asset B
= [0.112-0.04)2X0.35] + [0.112-0.04)2X0.50] + [0.112-0.04)2X0.15]
Variance of Asset C
= [(0.166-0.04)2X0.35] + [(0.166-0.04)2X0.50] + [(0.166-0.04)2X0.15]
c) Standard deviation
Standard deviation (SD) = variance
Standard deviation for asset A = 0 = 0
Standard deviation for asset B =0.005184 = 0.072
Standard deviation for asset C = 0.015876 = 0.126
- a) It is true that a correlation coefficient of zero indicates that there is no relationship between the two variables.
b) True. Correlation does not necessarily mean causation. Two variables may be correlated even if one does not cause the change in the other.
c) True. There is a linear relationship between X and Y since the correlation coefficient is not zero. A negative value implies that there X increases with a decrease in Y (Sharma 478).
- a) R-squared statistic indicates the coefficient of determination. It denotes the amount of variations in annual profit explained by changes in advertising expenditure (Black 508). In this case, Adjusted R-Square is 86.2% indicating that 86.2% of the changes in companies’ annual profit are explained by changes in advertising expenditure. This is high enough hence the model is reliable in estimating annual profits.
b) The two t-tests are used to test the null hypotheses that the coefficient and the intercept/constant are not statistically significant (Gordon 213).
Since the p-value is more than 0.05, we can conclude at 95% confidence level that it is not statistically significant and therefore not a good measure of annual profit when advertising expenditure is zero.
The p-value is less than 0.05 hence we can conclude at 95% that the coefficient is statistically significant hence a good predictor of annual profit per unit of advertising expenditure.
- Profits = 0.56 + 0.0135A
- P = 0.56 + 0.0135 × 35,000
= 0.56 + 472.5
- P = 0.56 + 0.0135 × 10,000
= 0.56 + 135
Black, Ken. Business statistics: for contemporary decision making. Hoboken, NJ: Wiley, 2009. Print.
Gordon, Rachel A.. Regression analysis for the social sciences. New York, NY: Routledge, 2012. Print.
Meyer, Donald J.. The economics of risk. Kalamazoo, Mich.: W.E. Upjohn Institute for Employment Research, 2003. Print.
Sharma, J.K.. Business statistics. New Delhi: Dorling Kindersley, 2007. Print.