What are The four asset classes? Explain.
- The four asset classes are:Shares: These instruments represent ownership in the company. Exchange of shares (Buying or selling) takes place on the stock exchange(Colonial First State Investments Limited, 2016). These are volatile assets with medium to high risk characteristics. Also, the average returns are also high. As you can see the returns are negative for certain years so they are to be dealt with carefully and proper study of the stock based on fundamentals and technical.
- Bonds: These are the least risky assets and the returns are also low. But these are more risky than the government bonds. These provides regular fixed payments (Coupon bonds) or a lump sum amount at maturity (zero-coupon bonds).
- Cash: The investment in instruments like bank bills and similar other securities is referred to as cash. These are highly liquid assets which are less risky than shares. They provide low risk income which is quite stable and is similar to regular interest payments.(Colonial First State Investments Limited, 2016)
- International Shares: These are the listed shares of the companies of other countries. As the performance of these shares is dependent on the performance of these companies in their respective economies, hence these are less affect by the Australian economy. International shares expands the ambit in terms of geographies and companies where the investment can be made. However, the performance is highly affected by the changes in the currency exchange rate and hence are highly volatile(Colonial First State Investments Limited, 2016).
Table 1:
|
Year
|
Australian Shares
% return (ex dividends)
|
Australian Bonds
% return
|
Cash Rate
% average return
|
International Shares
% return
|
|
1990
|
-20.1%
|
12.1%
|
14.8%
|
-18.7%
|
|
1991
|
22.2%
|
9.4%
|
10.3%
|
16.0%
|
|
1992
|
-6.0%
|
8.9%
|
6.5%
|
-7.1%
|
|
1993
|
39.1%
|
6.7%
|
5.1%
|
20.4%
|
|
1994
|
-9.2%
|
10.0%
|
5.4%
|
3.4%
|
|
1995
|
16.5%
|
8.2%
|
7.5%
|
18.7%
|
|
1996
|
7.2%
|
7.4%
|
7.0%
|
11.7%
|
|
1997
|
7.9%
|
6.1%
|
5.4%
|
14.2%
|
|
1998
|
7.7%
|
5.0%
|
5.0%
|
22.8%
|
|
1999
|
13.5%
|
7.0%
|
4.8%
|
23.6%
|
|
2000
|
2.9%
|
5.5%
|
6.0%
|
-14.1%
|
|
2001
|
2.6%
|
6.0%
|
4.9%
|
-17.8%
|
|
2002
|
-9.6%
|
5.2%
|
4.6%
|
-21.1%
|
|
2003
|
8.7%
|
5.6%
|
4.8%
|
30.8%
|
|
2004
|
22.8%
|
5.3%
|
5.3%
|
12.8%
|
|
2005
|
15.7%
|
5.2%
|
5.5%
|
7.6%
|
|
2006
|
19.8%
|
5.9%
|
5.8%
|
18.0%
|
|
2007
|
17.9%
|
6.3%
|
6.4%
|
7.1%
|
|
2008
|
-45.8%
|
4.0%
|
6.6%
|
-42.1%
|
|
2009
|
34.1%
|
5.7%
|
3.2%
|
27.0%
|
|
2010
|
2.2%
|
5.5%
|
4.4%
|
9.6%
|
Arithematic mean, geometric mean and standard deviation are as under
|
Arithmetic Mean (AM)
|
|
|
Australian Shares
|
7.1%
|
|
Australian Bonds
|
6.7%
|
|
Cash Rate
|
6.2%
|
|
International Shares
|
5.8%
|
|
|
Geometric Mean (GM)
|
|
|
Australian Shares
|
7.7%
|
|
Australian Bonds
|
7.0%
|
|
Cash Rate
|
6.0%
|
|
International Shares
|
-17.8%
|
|
|
Standard deviation (σ)
|
|
|
Australian Shares
|
18.7%
|
|
Australian Bonds
|
2.0%
|
|
Cash Rate
|
2.4%
|
|
International Shares
|
19.0%
|
|
As it can be seen from the AM, GM and standard deviation, Australian bonds are least risk and with minimum return, while Australian shares are most risky and with highest return. Geometric mean has been calculated using the GEOMEAN function in excel. Standard deviation has been calculated using STDEV function in excel.
|
Correlation matrix
|
Australian Shares
|
Australian Bonds
|
Cash Rate
|
International Shares
|
|
Australian Shares
|
1.00
|
(0.09)
|
(0.31)
|
0.81
|
|
Australian Bonds
|
(0.09)
|
1.00
|
0.74
|
(0.02)
|
|
Cash Rate
|
(0.31)
|
0.74
|
1.00
|
(0.30)
|
|
International Shares
|
0.81
|
(0.02)
|
(0.30)
|
1.00
|
|
Covariance matrix
|
Australian Shares
|
Australian Bonds
|
Cash Rate
|
International Shares
|
|
Australian Shares
|
0.033469
|
(0.000335)
|
(0.001340)
|
0.027664
|
|
Australian Bonds
|
(0.000335)
|
0.000373
|
0.000342
|
(0.000058)
|
|
Cash Rate
|
(0.001340)
|
0.000342
|
0.000568
|
(0.001317)
|
|
International Shares
|
0.027664
|
(0.000058)
|
(0.001317)
|
0.034428
|
Correlation and Covariance matrix has been computed using the CORREL and COVAR functions in excel.
For constructing the efficient frontier with three assets it has been assumed that short sales are not allowed. Solver has been used to determine the weights of the three assets in the portfolio. The standard deviation has been minimized for certain return value such that the sum of the weights is 100%.
| |
Efficient frontier with three assets
|
|
|
S. No.
|
portfolio return
|
W1(australian shares)
|
W2(australian bonds)
|
W3(Cash Rate)
|
variance of portfolio
|
Portfolio standard deviation (σ)
|
Return
|
|
|
|
Minimum Variance portfolio
|
2.68%
|
75.04%
|
22.28%
|
0.03%
|
1.864%
|
6.60%
|
|
|
1
|
6.61%
|
2.65%
|
76.58%
|
20.78%
|
0.03%
|
1.864%
|
6.61%
|
|
|
2
|
6.62%
|
2.60%
|
78.45%
|
18.95%
|
0.03%
|
1.864%
|
6.62%
|
|
|
3
|
6.63%
|
2.56%
|
80.32%
|
17.12%
|
0.03%
|
1.865%
|
6.63%
|
|
|
4
|
6.64%
|
2.52%
|
82.19%
|
15.29%
|
0.03%
|
1.867%
|
6.64%
|
|
|
5
|
6.65%
|
2.48%
|
84.06%
|
13.46%
|
0.03%
|
1.869%
|
6.65%
|
|
|
6
|
6.66%
|
2.44%
|
85.93%
|
11.64%
|
0.03%
|
1.871%
|
6.66%
|
|
|
7
|
6.67%
|
2.39%
|
87.79%
|
9.81%
|
0.04%
|
1.873%
|
6.67%
|
|
|
8
|
6.68%
|
2.35%
|
89.66%
|
7.98%
|
0.04%
|
1.876%
|
6.68%
|
|
|
9
|
6.69%
|
2.31%
|
91.53%
|
6.16%
|
0.04%
|
1.880%
|
6.69%
|
|
|
10
|
6.70%
|
2.27%
|
93.40%
|
4.33%
|
0.04%
|
1.884%
|
6.70%
|
| |
|
|
|
|
|
|
|
|
Let 5 be the efficient portfolio
| |
|
|
|
Return of portfolio
|
6.65%
|
|
|
Standard of portfolio
|
1.869%
|
|
|
Risk free rate
|
6.40%
|
|
|
weight of risky portfolio
|
combination return
|
Standard deviation
|
|
0
|
6.40%
|
0.000%
|
|
0.1
|
6.43%
|
0.187%
|
|
0.2
|
6.45%
|
0.374%
|
|
0.3
|
6.48%
|
0.561%
|
|
0.4
|
6.50%
|
0.747%
|
|
0.5
|
6.53%
|
0.934%
|
|
0.6
|
6.55%
|
1.121%
|
|
0.7
|
6.58%
|
1.308%
|
|
0.8
|
6.60%
|
1.495%
|
|
0.9
|
6.63%
|
1.682%
|
|
1
|
6.65%
|
1.869%
|
| |
|
|
|
|
Efficient frontier with four assets
|
Efficient frontier with four assets
|
|
portfolio return
|
W1
(australian shares)
|
W2
(australian bonds)
|
W3
(Cash Rate)
|
W4
(international Shares)
|
variance of portfolio
|
Portfolio standard deviation (σ)
|
Return
|
|
Minimum Variance portfolio
|
3.093%
|
76.156%
|
21.286%
|
-0.535%
|
0.035%
|
1.863%
|
6.614%
|
|
6.49%
|
2.349%
|
56.081%
|
40.645%
|
0.925%
|
0.036%
|
1.886%
|
6.490%
|
|
6.50%
|
2.409%
|
57.704%
|
39.080%
|
0.807%
|
0.035%
|
1.882%
|
6.500%
|
|
6.51%
|
2.469%
|
59.326%
|
37.516%
|
0.689%
|
0.035%
|
1.879%
|
6.510%
|
|
6.52%
|
2.529%
|
60.949%
|
35.951%
|
0.571%
|
0.035%
|
1.876%
|
6.520%
|
|
6.53%
|
2.590%
|
62.571%
|
34.387%
|
0.453%
|
0.035%
|
1.874%
|
6.530%
|
|
6.54%
|
2.650%
|
64.193%
|
32.822%
|
0.335%
|
0.035%
|
1.871%
|
6.540%
|
|
6.56%
|
2.770%
|
67.438%
|
29.693%
|
0.099%
|
0.035%
|
1.867%
|
6.560%
|
|
6.57%
|
2.830%
|
69.060%
|
28.129%
|
-0.019%
|
0.035%
|
1.866%
|
6.570%
|
|
6.58%
|
2.890%
|
70.683%
|
26.564%
|
-0.137%
|
0.035%
|
1.865%
|
6.580%
|
|
6.59%
|
2.951%
|
72.305%
|
25.000%
|
-0.255%
|
0.035%
|
1.864%
|
6.590%
|
|
6.60%
|
3.011%
|
73.927%
|
23.435%
|
-0.373%
|
0.035%
|
1.863%
|
6.600%
|
|
6.61%
|
3.071%
|
75.550%
|
21.871%
|
-0.491%
|
0.035%
|
1.863%
|
6.610%
|
|
6.62%
|
3.131%
|
77.172%
|
20.306%
|
-0.609%
|
0.035%
|
1.863%
|
6.620%
|
|
6.63%
|
3.191%
|
78.794%
|
18.742%
|
-0.727%
|
0.035%
|
1.863%
|
6.630%
|
|
6.64%
|
3.252%
|
80.416%
|
17.178%
|
-0.846%
|
0.035%
|
1.864%
|
6.640%
|
|
6.65%
|
3.312%
|
82.038%
|
15.613%
|
-0.964%
|
0.035%
|
1.865%
|
6.650%
|
|
6.66%
|
3.372%
|
83.661%
|
14.049%
|
-1.082%
|
0.035%
|
1.866%
|
6.660%
|
|
6.67%
|
3.432%
|
85.283%
|
12.484%
|
-1.200%
|
0.035%
|
1.868%
|
6.670%
|
|
6.68%
|
3.492%
|
86.906%
|
10.920%
|
-1.318%
|
0.035%
|
1.870%
|
6.680%
|
|
6.69%
|
3.552%
|
88.528%
|
9.355%
|
-1.436%
|
0.035%
|
1.872%
|
6.690%
|
|
6.70%
|
3.613%
|
90.150%
|
7.791%
|
-1.554%
|
0.035%
|
1.874%
|
6.700%
|
Effect of fiscal and monetary policy on the economy
Fiscal policy are the measures taken by the government to affect the supply of goods and services. Monetary policy are the measures taken to affect the money supply and interest rates. Monetary policy changes are generally taken by the central bank. These measures can be contractual and expansionary. For example if the government wants to increase the GDP, it will increase the spending in goods and services which increases demand. Increased demand causes companies to increase supply which improves employment (Grimsley, 2016). Increased employment increase the per capita income and also private consumption. In terms of fiscal policy, if the central bank reduces the interest rates the money supply increases which increase private consumption and the demand goes up. As the demand goes up and with limited supply in the short run, the prices go up and the inflation increases. In the long run, the firms are able to increase the supply of goods and services (Dornbusch, Fischer, & Startz, 2011). Aggregate demand AD is given by AD = C + G + I + NX. Where C is private consumption, G is government expenditure, I in investment and NX is net of exports and imports. As expansionary fiscal policy is followed, government expenditure increase and thus AD increases. As expansionary monetary policy is followed, money supply increases in the market thus increasing the private consumption and thereby increasing the aggregate demand (Investopedia, 2016).
|
Stock price (S0)
|
39
|
|
Exercise price (X)
|
35
|
|
Interest rate ( r )
|
5.30%
|
|
time to expiration (T)
|
0.5
|
|
Standard deviation (σ)
|
30%
|
| |
(ln(S0/X)+(r+σ^2/2)T)/(σ√T)
|
=0.741112
|
|
|
d2=
|
d1-σ√T
|
= 0.52898
|
|
|
N(d1)=
|
0.760737504
|
|
N(-d1)=
|
0.229338
|
|
N(d2)=
|
0.70152708
|
|
N(-d2)=
|
0.298473
|
| |
|
|
|
|
|
|
Call option Price, C=
|
N(d1)S0 - X(e^(-rT))N(d2)
|
| |
5.76
|
|
Put option price, P=
|
-N(-d1)*S0 + X(e^(rT)N(-d2)
|
| |
1.23
|
|
|
Contract size
|
100
|
|
|
|
|
Initial margin
|
10%
|
= $11979
|
|
|
|
Maintenance margin
|
5%
|
= $5989.5
|
|
|
Day
|
Trade Price($)
|
Futures Price
(US dollar per ounce)
|
Daily gain($)
|
Cumulative gain($)
|
Margin account balance($)
|
Margin call($)
|
|
8-Feb-2016
|
1197.90
|
|
|
|
11979
|
|
|
9-Feb-2016
|
|
1198.70
|
80.00
|
80.00
|
12059.00
|
|
|
10-Feb-2016
|
|
1194.70
|
-400.00
|
-320.00
|
11659.00
|
|
|
11-Feb-2016
|
|
1247.90
|
5320.00
|
5000.00
|
16979.00
|
|
|
12-Feb-2016
|
|
1239.10
|
-880.00
|
4120.00
|
16099.00
|
|
|
15-Feb-2016
|
|
1239.10
|
0.00
|
4120.00
|
16099.00
|
|
|
16-Feb-2016
|
|
1207.90
|
-3120.00
|
1000.00
|
12979.00
|
|
|
17-Feb-2016
|
|
1211.10
|
320.00
|
1320.00
|
13299.00
|
|
|
18-Feb-2016
|
|
1226.10
|
1500.00
|
2820.00
|
14799.00
|
|
|
19-Feb-2016
|
|
1230.40
|
430.00
|
3250.00
|
15229.00
|
|
|
22-Feb-2016
|
1209.50
|
|
-779.50
|
2470.50
|
17699.50
|
|
| |
|
|
|
|
|
|
|
|
|
Basis risk is the risk that the price of the future contract does not move in line with the underlying and thus the price changes are not exactly in opposite direction. It may arise:
- If the asset to be hedged is not exactly same as the futures contract’s underlying asset
- There is uncertainty on the part of the hedger on the date of buying or selling the asset
- Futures contracts may be closed before the delivery date(C.Hull, 2012)
It is defined as:
Basis risk = spot price of the asset – futures price of the contract
Difference between Options and future
The main difference lies in the obligation of execution. In options, the parties does not have the obligation to buy (or sell) the underlying assets where as in case of futures the parties are obliged to buy (or sell) the underlying assets (Difference between options and futures - Option Trading FAQ, 2016).
A futures contract can be entered into without any upfront cost while in case of options there is upfront premium that is to be paid.
The size of underlying is generally very large in case of futures as compared to options (C.Hull, 2012).
|
Portfolio performance data
|
|
|
Fund
|
Portfolio
|
Market
|
|
Average return
|
x
|
12%
|
8%
|
|
Beta
|
β
|
1.15
|
1
|
|
Standard deviation
|
σ
|
33%
|
25%
|
|
tracking error
|
σ( e)
|
14%
|
0
|
|
Sharpe ratio(portfolio)=
|
(Rp-Rf)/σp
|
0.19697
|
|
|
Sharpe ratio(Market)=
|
(Rm-Rf)/σm
|
0.1
|
|
|
Treynor measure=
|
(Rp-Rf)/βp
|
0.056522
|
|
|
Jensen's Alpha=
|
Rp-(Rf + βp(Rm-Rf))
|
0.03625
|
|
|
Information ratio=
|
(Rp-Rm)/σ( e)
|
0.285714
|
|
|
M2 measure=
|
Rf + (Rp-Rf)*(σm/σp)
|
0.073939
|
|
As the Sharpe ratio of the portfolio is more than the market, it is outperforming the market.
References
C.Hull, J. (2012). Options, Futures, And Other derivatives. New York: Prentice Hall.
Colonial First State Investments Limited. (2016, June 10). Investment asset classes: Cash, fixed interest, property and shares :: Colonial First State. Retrieved from Colonial First State: https://www3.colonialfirststate.com.au
Difference between options and futures - Option Trading FAQ. (2016, 06 07). Retrieved from The Options Guides: www.theoptionsguide.com
Dornbusch, R., Fischer, S., & Startz, R. (2011). Macroeconomics. New York: McGraw-Hill.
Grimsley, S. (2016, June 10). How Fiscal Policy and Monetary Policy Affect the Economy. Retrieved from Study.com: https://www.study.com
Investopedia. (2016, June 10). How do fiscal and monetary policies affect aggregate demand? Retrieved from Investopedia: https://www.investopedia.com
