Calculating Arithmetic Mean, Geometric Mean And Standard Deviation Of Different Asset Classes

Arithmetic mean

Calculate the Arithmetic mean, Geometric mean, Standard deviation of four different asset classes.
 

This assignment is fully consisting of calculating the Arithmetic mean, Geometric mean, Standard deviation of four different asset classes. It also shows the risk return characteristics of these different classes of assets in the portfolio. This assignment also shows the effect of fiscal and Referencingonetary policy in the economic condition as well as the factors that determines the sensitivity of the firm’s earnings on the business cycle. this assignment also consist of calculation based on the black scholes model, difference between futures and options, calculation of daily market to market settlements and measuring the performance of the portfolio using the various methods such as Sharpe, Treynor method, Jeanson Alpha. 

Arithmetic mean can be defined as the measure of central tendency of the sample which can be computed by dividing the total of the data in the table by the number of data in the table. It is actually the average of the given data. Geometric mean can be defined as the n^th root of the product n, which is much different from that of the arithmetic mean. Standard deviation (σ) can be defined as the measure which is usually used for quantifying the sum of deviation. If the value of standard deviation is low it means that the actual value is very close to the expected value but if the value of standard deviation is high it represents that the actual value is far away from the expected value.

For Australian shares

mean	7.147619
G.Mean	11.67384
S.D	18.74643

For Australian Bonds

mean	6.714286
G.Mean	6.474475
S.D	1.979719

For Cash Rates

mean	6.157143
G.Mean	5.832839
S.D	2.441223

For international shares

mean	5.847619
G.Mean	15.76595
S.D	19.01293

From the calculation it has been seen that the arithmetic mean of the Australian shares, Australian bonds, cash rates and international shares are 7.147619, 6.714286, 6.157143, and 5.847619 respectively. The arithmetic mean is highest in Australian bonds and lowest in international shares. The geometric mean of the Australian shares, Australian bonds, cash rates and international shares are 11.67384, 6.474475, 5.832839, and 15.76595 respectively. The geometric mean is highest in international bonds and lowest in cash rates. The standard deviation of Australian shares, Australian bonds, cash rates and international shares are 18.74643, 1.979719, 2.441223, and 19.01293 respectively. The standard deviation is highest in international shares which mean that the actual value is far away from the expected value and the lowest value is Australian bonds which mean that the actual value is very close to the actual value.

Bordered Covariance
	Australian Shares % return (ex dividends)	Australian Bonds % return	Cash Rate % average return
Australian Shares % return (ex dividends)	334.6939	-3.3483	-13.3961
Australian Bonds % return	-3.3483	3.732653	3.422517
Cash Rate % average return	-13.3961	3.422517	5.675782

Correlation Matrices
	Australian Shares % return (ex dividends)	Australian Bonds % return	Cash Rate % average return
Australian Shares % return (ex dividends)	1	-0.09473	-0.30735
Australian Bonds % return	-0.09473	1	0.743574
Cash Rate % average return	-0.30735	0.743574	1

expected weight	0.34762075
sd	4.45434258
sharp	-1.4126393
cal	-0.0317138

For four assets

Bordered Covariance
	Australian Shares % return (ex dividends)	Australian Bonds % return	Cash Rate % average return	International Shares % return
Australian Shares % return (ex dividends)	4.111105	0.170998	0.067995	1.734405
Australian Bonds % return	0.170998	0.051819	-0.00797	0.104407
Cash Rate % average return	0.067995	-0.00797	0.050475	0.141441
International Shares % return	1.734405	0.104407	0.141441	4.584085

Correlation Matrices
	Australian Shares % return (ex dividends)	Australian Bonds % return	Cash Rate % average return	International Shares % return
Australian Shares % return (ex dividends)	1	0.370482	0.149265	0.399526
Australian Bonds % return	0.370482	1	-0.15574	0.21422
Cash Rate % average return	0.149265	-0.15574	1	0.294044
International Shares % return	0.399526	0.21422	0.294044	1

expected weight	1.070197
sd	0.908985
sharp	-6.1275
cal	-0.6741

The investments that are made by the individuals are broadly classified into two broad heads such as growth assets and defensive assets. Growth assets are those assets which are mainly planned for the growth of the investment of the individuals. These investments include shares, property, substitute investments etc. defensive assets are those assets which comprises of the investment in cash and fixed interest. These assets have lower risk as a result of which it generates lower return. For the growth assets, higher risk will indicate higher return where as for defensive assets; lower risk will indicate lower return ("Asset classes explained", 2016).

Geometric mean

For the shares which indicates the ownership of the individual in the company, the return of which comes from the increase or decrease in the share price as well as the dividend received by the shareholders out of the profits of the company. For the cash which is a defensive asset, the return comes from the interest rates on the money which is deposited in the bank as from the short term money market securities. For the bonds which is also a defensive assets the return comes from the interest on the amount of the loan as well as the increase and decrease in the value of the underlying securities.

During 1930s, there was an immense depression which has influenced the political and economic thoughts of the country. The economic stability is generally been preferred by the house holds during short run, which allows them to continue steady consumption with the help of continuous service & stable income. Whereas, growth can be reduced due to unnecessary fluctuations in the economic conditions during long run.

Fiscal policy is a short of decision of the government about the expenditure as well as the taxing. When the government is willing to increase the expansion in the economy then the government will have to increase the expenditure on goods and services. As a result the demand for goods and services gets increased. On the other hand, if the economy is growing rapidly as per the government then the government can curtail down its expenditure. If the government reduces its expenditure the demand prevailing in the economy will also gets decreased. Payment of tax to the government is another side of the fiscal policy. If the tax rates get reduced it indicates that it will motivate to increase the growth in the economy (Auerbach, 2003).

Some economists think that there will be a crowding out effect in the economy due to the expenditure incurred by the government and reduction in tax rates. The government will have to lend money if the sufficient amount is not available with the government for doing expenditure. As per the economist, government lending increases the interest rates which in turn dishearten the individual for the investment. Economist thinks that expenditure incurred by the government may crowd out the investment done by the individual as well as the business.

Again if the government wants to reduce the economy from overheating then it can increase the tax rates. This will result in the less spending of money, little number of people will be hired and ultimately the economy will slow down

Monetary policy is a kind of decision that the government takes for the supply of money as well as interest rates. Therefore the monetary policy plays an important role in controlling the growth of the economy via various channels. The stability of the price can be maintained which helps in sustainable growth in the economy (Fender, 2012). Constant boost in the price level is used as an effective tool by the monetary policy to control the supply of money in maintaining stability of price during the medium to long term. In other way it can be said that economic performance is getting damaged due to high inflation in long run. Expectations about the economic activities and the inflation rates are highly influenced by the monetary policy which in turn affects the prices of assets and commodities, consumption, exchange rates and investments. Financing situation of the economy is also affected by the monetary policy of the country (Mankiw, 2002).

Standard deviation

The decision taken in the monetary policy helps to reduce the interest rates which at last results in the increase in the investments and buying of consumable products also get increased. When the low interest rates are prevailing in the market, it becomes more attractive to purchase the stocks as well as the low interest rates may cause depreciation in the currency. Thus it may be seen that the output may be increased due to the various combination of above mentioned factors (Persson, 2000)

Three main factors determining the sensitivity of firm’s income on business cycle

Most of the times it has been seen that the economy of the country faces well as well as a bad situation. This phase of depression as well as improvement is commonly known as business cycle. Though economy of the country faces various stages of the cycle of the business, therefore, it has been noticed that the relative performance will expected to vary from industry to industry. It has been seen that cyclic industries performs very well during improvement phase where as the defensive industries smash up other industries during depression phase.

Once the economist analyse the state of economy prevailing in the country, then it becomes mandatory to determine the sensitivity of the firm’s earnings on business cycle. The factors are as follows:-

• Sensitivity to sales:- Necessary items like foods, medicine etc will have a very low sensitivity in relation to the business conditions. On the other hand, transportation, machine tools etc have high sensitivity in relation to sales.
• Operating leverage:- It shows the separation between the variable cost as well as the fixed cost. A firm with greater amount of variable cost as compared to fixed cost will be termed as not as much sensitive to business conditions. On the other hand, the firm having higher amount of fixed cost will move to and fro more extensively with sales.
• Financial leverage:- The payment of interest on debt have to be paid in spite of higher amount of sales. The payment of interest causes drainage of profit. As the payment of interest is treated as fixed cost which results in the increasing the sensitivity of profit to business conditions. 

The black schole model is a model which is used for pricing the European options as well as the derivatives. It is basically the option pricing model which helps in the determination of value for call or put options. The Black-Scholes formula is used to calculate the current value of a European call option on a stock which pays no dividends before expiration of the option (Birge and Linetsky, 2008). The formula of this model is as follows:-

The detailed of the calculation are as follows:-

s	39	t	0.5		sigma	0.3
r	0.053	x	35

d1	0.296598
d1	0.084466

call options

21.68393

Maintenance margin = 5% of ($1197.90*100)

                                   = $5989.5

Initial margin = 10% of ($1197.90*100)

                                  = $11979 

Days	Future Price	Profit or loss	Initial Margin	Maintenance Margin	Margin call	Value
8.02.16	$119,790	$80	$11,979	$5,989.50	-	$80
9.02.16	$119,870	($400)	-	-	-	$80-$400= ($320)
10.02.16	$119,470	$5,320	-	-	$5989.50-$4910 = $1079.5	($320)+$5230= $4910+$1079.5 = $5989.5
11.02.16	$124,790	($880)	-	-	$5989.50 - $5109.5 = $880	$5989.5 + ($880) = $5109.5 + $880 = $5989.5
12.02.16	$123,910	$0	-	-	-	$5989.5+$0 = $5989.5
15.02.16	$123,910	($3,120)	-	-	$5989.5 - $2869.5 = $3120	$5989.5+($3120)= $2869.5 + $3120 = $5989.5
16.02.16	$120,790	$320	-	-	-	$5989.5+$320 = $6309.5
17.02.16	$121,110	$1,500	-	-	-	$6309.5+$1500 = $7809.5
18.02.16	$122,610	$430	-	-	-	$7809.5+$430 = $8239.5
19.02.16	$123,040	($2,090)	-	-	-	$8239.5+ ($2090)= $6149.5
22.02.16	$120,950	$0	-	-	-	$6149.5+$0 = $6149.5

Difference between futures and options

In option the buyer has the right to purchase the shares but the purchaser does not have the obligation. As a purchaser he or she has the right to choose the call option or put option but as the seller of the option he or she has only obligation. There are two types of options such as call option as well as put option. Future can be defined as the contract between the two parties for purchasing and selling specific assets at a certain time in future at a certain rate. Buyer and seller both has the obligation in completing the contract at a certain price and at a certain date in future. On the other hand in option, the buyer can opt for completion of contract but he or she is not bound to complete the option where the seller is bound to sell the contract. In future there is a specified date within which the contract must be completed. But in options the contract can be completed in any time before the contract expires. The most important difference between future and option is that option can be exercised before maturity where as the future is exercised after maturity (Neftci, 2004). 

Sharpe ratio is mainly build by William F. Sharpe which can be defined as the ratio of portfolio return reduced by the risk free rate of return whole divided by standard deviation (Brentani, 2004). The main objective of sharpe measure is to point out how well the equity investments are performing in comparison to the risk free rate of return. The purpose of calculating the sharpe ratio is to focus on how the individual is getting greater return after accepting the greater risk which is the inbuilt feature of the equity investment in comparison to risk free rate of investment.

Speared ratio for fund portfolio

= (12-5.5)/33

=0.196

=19.6%

Speared ratio for market portfolio

= (8-5.5)/25

=0.1

=10%

Treynor ratio is mainly developed by the Jack L. Treynor which measures the return earned over and above the actual earnings. The Treynor ratio focuses on the evaluation of return of the investment comprising of the risk portfolio. Treynor basically focuses on how efficiently the portfolio is performing in the equity market.

Treynor ratio for fund portfolio

= (12-5.5)/1.15

=5.652

= 562.2%

Treynor ratio for market portfolio

= (8.5.5)/1.

=2.5

=250%

Jeanson alpha measure is the performance measure which shows the risk associated with the assets and is calculated with the help of the capital asset pricing model. It is also used to determine the excess return on the investment by using the capital asset pricing model. Security market line is used as the benchmark in this measure. The main purpose of this model is to reduce the value of beta so that there is an expectation of having the higher return on the risky assets. Choosing the market index is the important point in this measure as the market portfolio is measured with the performance of the portfolio.

Alpha=12-(5.5+1.15(  8-5.5) =3.625 

Auerbach, A. (2003) Fiscal policy. 2nd edition. Cambridge, Mass.: MIT Press.

Birge, J. & Linetsky, V. (2008) Financial engineering. Amsterdam: North-Holland.

Brentani, C. (2004) Portfolio management in practice. Oxford [England]: Burlington, MA.

Cooper, R. et al. (1998) Portfolio management for new products. Reading, Mass.: Addison-Wesley.

Fender, J. (2012) Monetary policy. Hoboken, N.J.: Wiley.

Mankiw, N. (2002) Monetary policy. 2nd edition. Chicago: University of Chicago Press.

Neftci, S. (2004) Principles of financial engineering. San Diego, Calif.: Elsevier Academic Press.

Persson, T. (2000) Monetary and fiscal policy. 2nd edition. Cambridge, Mass.: MIT Press.