英国论文代写网

当前位置: 首页 > 精品范例 > 加拿大论文代写essayassignment
加拿大论文代写essayassignment

加拿大温哥华代写市场骗子充斥,高分截图说明才是真道理,sfu高分金融会计案例公示profolio accounting&finance

  • 国家 : 加拿大
  • 级别 : 硕士
  • 专业 :
能做将近满分的金融计算作业不是盖的,内容看看各位心里就有数了,加上截图证明我们的实力一目了然!

详细描述

代写声明:为了保护版权,只做部分展示

1.      Introduction

In face of huge quantities of securities in stock market, deciding which security portfolio tend to bring higher returns is annoying. This research will give inventors a rough expression that how to allocate portfolio withMarkowitz’s modern theory. First part will illustrate several instruments in deducing Markowitz efficient frontier, containing basic kinds of return and risk of single stock and portfolio. Meanwhile, the benefit of diversification will be well demonstrated.

 

2. Primary assumptions

l   Every inventor is a rational person with an objective to expected mean return  with minimum risks. Every investor pursues maximum value.

l   With respect to yield of stocks, transaction expense is taken no account. It will simplify the process of allocating portfolio.

l   Suppose market is efficient without arbitrage behavior.

 

2.1Portfolio construction

In order to illustrate the Markowitz’s modern portfolio theory, three stocks concerned with three totally different sectors have been chosen. One of the stocks is combined with the most popular corporation British American Tobacco, whose major business is related to producing tobacco as well as distributing cigarettes. The second security is related to Capital Shopping Centres Group PLC, a global shopping centre owning 14 regional branches. Due to its significant in size, PLC shares a steady growth rate of 0.1% and a low variance of 2.8% during past 9 years. Associated British Foods plc also enjoys great popularity in the field of food retailing. With various Bata of three stocks ,it is possible to hedge risk. The efficient frontier does not include zero dispersion assets, so the treasury bond is not taking into account.

 

2.2A single security’s yield and risk

As sufficient historical data is provided on Yahoo Finance, it is convenience to employ statistics calculating all the characteristic of stocks of BATS.L, CSCG.L, ABF.L.

 

Mean return gives an average return an inventor expected to earn before the event. In the case of BATS.L, monthly mean return from 2003/7/1 to 2012/11/1 is calculated as the average of all the twelve monthly returns.

Sample mean return monthly=      =                             =4.49%

Annually nominal return for BATS.L is easily calculated as the monthly mean return (4.49% ) multiplied by 12. High yield is an appealing factor in choosing stocks.

                     =4.49%×12=53.88%

Table1 . historical data and rate of return of three stocks

Date

BATS.L

CSCG.L

ABF.L

BATS.L

CSCG.L

ABF.L

 

Historical data

 

 

   Rate of return

 

2012/11/1

3074.5

335.6

1394

0.00162893

0.007807808

0.006498

2012/10/1

3069.5

333

1385

-0.034596635

0.031630472

0.074476

2012/9/3

3179.5

322.79

1289

-0.0369529

-0.031387847

-0.02644

2012/8/1

3301.5

333.25

1324

-0.028256071

0.048747482

0.05498

2012/7/2

3397.5

317.76

1255

0.048125868

0.000314802

-0.02106

2012/6/1

3241.5

317.66

1282

0.059833252

0.042738971

0.079125

2012/5/1

3058.5

304.64

1188

-0.031813865

-0.025775504

-0.02543

2012/4/2

3159

312.7

1219

0.002697984

-0.019318823

-0.00082

2012/3/1

3150.5

318.86

1220

0.493736784

-0.003904908

0.018364

2012/2/1

2109.14

320.11

1198

0.089133657

0.029391903

0.039029

2012/1/3

1936.53

310.97

1153

-0.045329508

0.034910809

0.041554

*Data collected from yahoo finance

 

2.1.2Risk

In the field of portfolio selection, variance and probability of an adverse outcome are three best-known mathematical definitions of risk( XiaoxiaHuang, 2008).

BATS.L deviation from mean in Jua-12 is (0.73%-4.49%  =14.14%

 

 
 

 

 

 

The variance of the expected return of asset I is demonstrated as

Standard Deviationcan be calculated as the positive square root of sample variance.

By the means of formula, the standard deviation of BATS.L is 14.76%.

 

Through this method, the variance of the expected return of three enterprise is below.

 

Table2. mean, variance & volatility of three enterprises.

 

 

           BAST.L

       CSCT.L

ABS.L

Mean

 

0.04492732

0.000113586

0.009821

Variance

 

0.021793294

0.000863006

0.00141

Volatility

0.147625519

0.029376971

0.037554

Respectively, mean return and variance of three enterprises show the tendency that high risk deserves high revenue.

 

 

2.2The characteristics of portfolio

 

2.2.1Expected return of portfolio

For example, BATS.L counts 90%, CSCG.L counts 5%, ABF.L counts 5%, the expected return is 4.09%.

The expected return of portfolio is a simple linear combination of individual asset whose weight isthe value of a single asset of the percentage of the total value. Considering three enterprise’s historical data, different weight of each stock results in different revenue and risk of portfolio. The approach to deciding weight of individual stock is what Mean-Variance methodology illustrates.

 

2.2.2Risk of portfolio

 

Covariancestands for the correlation coefficient of every part of two assets. When covariance is a negative number, it makes sense to include these two assets in a portfolio because of risk diversification. Specifically, suppose stock A and B have a negative covariance, when market suffers a recession, stock A reached its lowest degree while stock B kicks its highest degree, then theunsystematic risk may reduce.

Covariance is formulated as

 

 

Table3covariance between each two stocks  

 

BATS.L

CSCG.L

ABF.L

BATS.L

 

0.2092506

0.93373536

CSCG.L

0.2092506

 

0.319402078

ABF.L

0.093373536

0.319402078

 

*Original data is collected from yahoo finance

The covariance between BATS.L and CSCG.L is 0.02093. A positive covariance refers to the positive correlation between them,indicating the unsystematic risk will not be diversified.

  

Variance of portfolio

Variance is a measure of how far a set of numbers is spread out and it also reflects the risk of assets. The variance of portfolio depends on both the weight of individual asset and the covariance of each two-asset group. This is a representative of portfolio risk. If BATS.L counts 90%, CSCG.L counts 5%, ABF.L counts 5%, the variance of portfolio will be 1.76%. From the calculation, we can find the variance of the portfolio, which is diversified with three assets, is much less than the variance of each single asset. Thus, risk-averse investor will diversify with portfolios at least some extent or completely.

 

 

2.3.0Caculating

Employing instruments below, a series of outcomes on BATS.L, CSCG.L & ABF.L emerge.

 

2.4.1Use combined means and portfolio variance for three-asset portfolio to construction feasible sets.

 

Table4portfolio return and variance of different weight of three stocks.

BATS.L

CSCG.L

ABF.L

Portfolio Return

Portfolio Variance

100%

0%

0%

0.04492732

0.021793294

90%

5%

5%

0.040931301

0.017636294

90%

1%

9%

0.041319585

0.017669092

90%

9%

1%

0.040543017

0.017604491

90%

2%

8%

0.041222514

0.017660799

90%

8%

2%

0.040640088

0.017612349

90%

3%

7%

0.041125443

0.017652569

90%

7%

3%

0.040737159

0.017620268

90%

4%

6%

0.041028372

0.0176444

90%

6%

4%

0.04083423

0.01762825

(More details is in Appendix I)

Through table 4, it is obvious that as the growing percentage of BATS.L combining with the reducing percentage accordingly in portfolio returns go up while portfolio variances go up, too. Because of positive correlation coefficient between BATS.L and CSCG.L, portfolio variance is not lower than each single asset.

Chart1

 

Applying statistics in the table to formulate a pattern, feasible set appears. The spot in the most left side along line is Minimum Variance Portfolio. Relatively, the other part below the point of Minimum Variance Portfolio is not efficient comparably. To verify this is making a vertical line from 0.001 point in horizontal axis and observing two crossing points. They possess same risk but the upper point enjoys higher rate of return. Hence, as a rational person, optimum portfolio one selects is along feasible line upper the spot of Minimum Variance Portfolio. It assumes that there is a portfolio which gives both maximum expected return and minimum variance, and it commends this portfolio to the investors (Markowitz, 1952)

 

Every two assets possess a positive covariance, which does not contribute to a much low rate of portfolio risk.

 

From Chart1, the pattern also comes from the statistics from table 4. Similarly, the value of BATS.L in portfolio goes down from 100% to 0%, while the values of CSCG.L & ABT.L go up at an inconsistent rate from 0%.

 

In conclusion, feasible set of portfolio represents all the possible combination of risky assets with different weights.

 

The pattern of Markowitz efficient frontier lies on the left boundary of feasible set and upper the spot ofMinimum Variance Portfolio. Every spot in the Markowitz efficient frontier satisfies the desire to every inventor who has a preference for the same level in return with the lowest rate in risk as well as the same level in risk with the highest rate in return..

 

2.4.3How to select optimal portfolio

Indifferent curve is a line in the return and risk plane, which provides the same utility to investors via a series of different returns and risks. It is a proper level of measurement of inventors’ utilities.

In the absence of riskless asset, a correspondence can be established between the safety-first criterion and expected utility maximization results in concave indifferent curves in the mean-standard deviation space (David H. Pyle and Stephen J. Turnovsky)

 

2.5.1Indifference curve

Provided that inventors are risk aversion (refer to assumption I), indifference curve exhibits a shape with an increasing slope. Indifference curve has many characteristics, such as two curves standing for different utility will not cross. The curve owning a longer distance from horizontal axis provides inventors higher utility.

 

    E(r)

                    

 

 

 
 

 

 

 

                     

 

 

 
 

 

 

 

2.5.2Choosing optimal portfolio for two-asset portfolio

Chart 2

线形标注 2(无边框): MVP

Pink line and orange line represents indifferent curve indicating the utility of investor while the blue line shows feasible set of two-asset portfolio. Then the optimal portfolio, that is to say, the portfolio bringing inventors most contents, just located in the crossing point of two lines.(indifferent curve varies from people to people and depends on one’s risk tolerance) Consequently, all kinds of indifferent curve emerge in the market. Different person has distinct portfolio allocation.

 

2.5.3Choosing optimal portfolio for three-asset portfolio

Chart 3

线形标注 2(无边框): Markowitz efficient frontier

 

Why three-asset portfolio’s feasible set looks like an umbrella not a single curve? Simply, weight plays a significant role in deciding the two shapes. Taking two assets into consideration, as the weight of one security floats, the other’s weight is certainty.

On the other hand, thinking over a scene with three securities, it is impossible to determine the other two securities as the weight of one security floats up and down.

 

2.5.4A summary on Markowitz’s modern portfolio theory

‘My 1952 article on portfolio selection proposed expected (mean) return(E) and variance of return(V)of the portfolio as a whole as criteria for portfolio selection should figure out Markowitz efficient frontier according to mean returns and variances of every single security and invest his assets based on efficient frontier. In addition, for the purpose ofminimizeunsystematic risk, investors had better to diversify assets over different sectors. One of the methods to distinguish the interdependence among various stocks is calculate covariance between each two assets.

 

No riskless securities includeMarkowitz devoted all his energy to allocating risk assets, regardless of risk-free stocks, the fundamental of market. In the following research, it is true that allocating part of investment in risk-free stocks does improve efficient frontier both in increasing yields and decreasing risk.

 

Too strong assumptionsAll the theory is processing under the assumption that prohibiting securities and risk-free lending. Practically, the assumption is too hard to reach, particularly, in the market with rapid pace of international lending. The operating principle should be that, to the extent that reliable information is available, it should be included as part of the optimization procedure (Michaud, 1989).

 

Is not adapt to single stockMarkowitz efficient frontier is only applied to select security portfolio. In terms of other fields, individual stock, for example, it is at a loss.

 

Unsuitable for specific evaluation When talking about utility function as well as indifference curve, investors lacking a sufficient application to measure one’s own utility. Thus, allocating each asset accurately is an annoying question. In portfolio selection problem, the expected return, risk, liquidity etc. cannot be predicted precisely. The investor generally makes his portfolio decision according to his experience and his economic wisdom (Rupak, 2011).

 

3.0Conclusion

 

This article lays emphasis on allocating optimal portfolio under the assumption that every investor is a risk aversion man, which deciding the location of efficient frontier. It stretches by the means ofthree stocks influenced by completely different factors. BAST.L has a good match to the assumption because of its high return and steady risk. In spite of this, the portfolio with most utilities can be found out by putting indifferent curve and efficient frontier together. The crossing point is optimal portfolio owning proper allocation. Last part points out several limitations on Markowitz’s modern theory. However, for more than three assets, the general approach has been to display qualitative results in terms of graphs (Merton, 1972).

 

4.0Reference
Markowitz. (1999) ‘An Early History of Portfolio Theory’, Financial Analysts Journal, vol.55, no.4, pp5-16

Michaud. (1989) ‘The Markowitz Optimization Enigma: Is ‘Optimized’ optimal?’ , Financial Analysts Journal, vol.45, no.1, pp31-42

Merton. (1972) ‘An Analytic Derivation of the Efficient Portfolio Frontier’, Cambridge Journal [Online] Available at: http://journals.cambridge.org/action/displayAbstract;jsessionid

Markowitz. (1952) ‘Portfolio Selection’, The Journal of Finance, vol.7, no.1, pp77-91 

Rupak. (2011) ‘Fuzzy mean–variance–skewness portfolio selection models by interval analysis’, Computers& Mathematics with application, vol.61, no.1, pp126-137

Steuer. (2007) ‘Randomly generating portfolio-selection covariance matrices with specified distributional characteristics’, European Journal of Operational Research, vol.177, no.3, pp1610-1625

XiaoxiaHuang. (2008) ‘Portfolio selection with a new definition of risk’, European Journal of operational research, vol.186, no.1 pp351-357

David H. Pyle and Stephen J. Turnovsky, ‘Safety-First and Expected Utility Maximization in Mean-Standard Deviation Portfolio Analysis’ The Review of Economics and Statistics Vol. 52, No. 1 (Feb., 1970), pp. 75-81

 

 

 

 

 

 

 

 

 

 

 

 

Appendix I

BATS.L

CSCG.L

ABF.L

Portfolio Return

Portfolio Variance

100%

0%

0%

0.04492732

0.021793294

90%

5%

5%

0.040931301

0.017636294

90%

1%

9%

0.041319585

0.017669092

90%

9%

1%

0.040543017

0.017604491

90%

2%

8%

0.041222514

0.017660799

90%

8%

2%

0.040640088

0.017612349

90%

3%

7%

0.041125443

0.017652569

90%

7%

3%

0.040737159

0.017620268

90%

4%

6%

0.041028372

0.0176444

90%

6%

4%

0.04083423

0.01762825

90%

0%

10%

0.041416656

0.017677446

90%

10%

0%

0.040445946

0.017596696

95%

1%

4%

0.043074917

0.019669317

95%

4%

1%

0.042783704

0.019644658

95%

2%

3%

0.042977846

0.019661035

95%

3%

2%

0.042880775

0.019652815

95%

0%

5%

0.043171988

0.019677661

95%

5%

0%

0.042686633

0.019636562

85%

1%

14%

0.039564254

0.015784286

85%

14%

1%

0.038302331

0.01568119

85%

2%

13%

0.039467183

0.015775983

85%

13%

2%

0.038399402

0.015688747

85%

3%

12%

0.039370112

0.015767741

85%

12%

3%

0.038496473

0.015696367

85%

4%

11%

0.039273041

0.015759562

85%

11%

4%

0.038593544

0.015704049

85%

5%

10%

0.03917597

0.015751445

85%

10%

5%

0.038690615

0.015711793

85%

15%

0%

0.03820526

0.015673694

85%

0%

15%

0.039661325

0.015792652

80%

10%

10%

0.036935283

0.013942309

80%

20%

0%

0.035964573

0.013867558

80%

0%

20%

0.037905993

0.014023277

75%

25%

0%

0.033723886

0.012178286

75%

0%

25%

0.036150661

0.012369321

75%

10%

15%

0.035179951

0.012288245

75%

15%

10%

0.034694596

0.012250038

74%

5%

21%

0.03531424

0.012011054

74%

21%

5%

0.033761104

0.011889255

74%

6%

20%

0.035217169

0.012002976

74%

20%

6%

0.033858175

0.011896401

74%

7%

19%

0.035120098

0.011994959

74%

19%

7%

0.033955246

0.011903609

74%

8%

18%

0.035023027

0.011987005

74%

18%

8%

0.034052317

0.01191088

74%

9%

17%

0.034925956

0.011979113

74%

17%

9%

0.034149388

0.011918213

74%

11%

15%

0.034731814

0.011963515

74%

15%

11%

0.03434353

0.011933065

70%

0%

30%

0.034395329

0.010830784

70%

30%

0%

0.0314832

0.010605879

70%

20%

10%

0.032453909

0.010674632

70%

10%

20%

0.033424619

0.0107496

65%

5%

30%

0.032154642

0.009366244

65%

30%

5%

0.029727868

0.009182437

65%

10%

25%

0.031669288

0.009326375

65%

25%

10%

0.030213223

0.009216091

65%

15%

20%

0.031183933

0.00928806

65%

20%

15%

0.030698578

0.009251298

65%

0%

35%

0.032639997

0.009407667

65%

35%

0%

0.029242513

0.009150338

62%

11%

27%

0.030519018

0.008520047

62%

27%

11%

0.028965882

0.008403798

62%

12%

26%

0.030421947

0.008512315

62%

26%

12%

0.029062953

0.008410598

62%

13%

25%

0.030324876

0.008504646

62%

25%

13%

0.029160024

0.008417459

62%

14%

24%

0.030227805

0.008497038

62%

24%

14%

0.029257095

0.008424383

60%

20%

20%

0.028943246

0.007943384

60%

5%

35%

0.030399311

0.008058492

60%

35%

5%

0.027487181

0.007842261

60%

15%

25%

0.029428601

0.007980199

60%

25%

15%

0.028457891

0.007908122

60%

10%

30%

0.029913956

0.008018569

60%

30%

10%

0.027972536

0.007874414

60%

40%

0%

0.027001826

0.007811661

60%

0%

40%

0.030884666

0.00809997

50%

50%

0%

0.022520453

0.005484902

50%

0%

50%

0.027374002

0.005830833

50%

30%

20%

0.024461873

0.005604627

50%

20%

30%

0.025432582

0.005673813

50%

10%

40%

0.026403292

0.005749215

50%

15%

35%

0.025917937

0.005710737

50%

35%

15%

0.023976518

0.005572365

50%

25%

25%

0.024947227

0.005638443

50%

45%

5%

0.023005808

0.005512503

50%

5%

45%

0.026888647

0.005789247

50%

40%

10%

0.023491163

0.005541657

40%

50%

10%

0.019009789

0.003676359

40%

10%

50%

0.022892629

0.003941539

40%

40%

20%

0.019980499

0.003733331

40%

20%

40%

0.021921919

0.00386592

40%

5%

55%

0.023377984

0.003981679

40%

55%

5%

0.018524434

0.003650204

40%

15%

45%

0.022407274

0.003902953

40%

25%

35%

0.021436564

0.003830442

40%

35%

25%

0.020465854

0.003764147

40%

45%

15%

0.019495144

0.003704068

40%

30%

30%

0.020951209

0.003796518

30%

45%

25%

0.015984481

0.002357311

30%

25%

45%

0.0179259

0.002484118

30%

40%

30%

0.016469836

0.002386682

30%

30%

40%

0.017440545

0.002450086

30%

35%

35%

0.01695519

0.002417607

30%

50%

20%

0.015499126

0.002329494

30%

20%

50%

0.018411255

0.002519705

30%

5%

65%

0.01986732

0.002635789

30%

65%

5%

0.014043061

0.002255366

30%

15%

55%

0.01889661

0.002556846

30%

55%

15%

0.015013771

0.00230323

30%

10%

60%

0.019381965

0.00259554

30%

60%

10%

0.014528416

0.002278521

30%

70%

0%

0.013557706

0.002233764

30%

0%

70%

0.020352675

0.002677591

20%

5%

75%

0.016356656

0.001751576

20%

75%

5%

0.009561687

0.001327987

20%

10%

70%

0.015871302

0.00171122

20%

70%

10%

0.010047042

0.001348143

20%

15%

65%

0.015385947

0.001672417

20%

65%

15%

0.010532397

0.001369853

20%

20%

60%

0.014900592

0.001635168

20%

60%

20%

0.011017752

0.001393117

20%

25%

55%

0.014415237

0.001599472

20%

55%

25%

0.011503107

0.001417934

20%

30%

50%

0.013929882

0.001565331

20%

50%

30%

0.011988462

0.001444306

20%

35%

45%

0.013444527

0.001532744

20%

45%

35%

0.012473817

0.001472231

20%

40%

40%

0.012959172

0.001501711

10%

0%

90%

0.013331348

0.001371061

10%

90%

0%

0.004594959

0.000852466

10%

5%

85%

0.012845993

0.001329041

10%

85%

5%

0.005080314

0.000868068

10%

80%

10%

0.005565669

0.000885225

10%

10%

80%

0.012360638

0.001288576

10%

15%

75%

0.011875283

0.001249665

10%

75%

15%

0.006051024

0.000903935

10%

70%

20%

0.006536379

0.000924199

10%

20%

70%

0.011389928

0.001212308

10%

70%

20%

0.006536379

0.000924199

10%

25%

65%

0.010904573

0.001176504

10%

65%

25%

0.007021734

0.000946017

10%

30%

60%

0.010419218

0.001142255

10%

60%

30%

0.007507089

0.00096939

10%

35%

55%

0.009933863

0.001109559

10%

55%

35%

0.007992444

0.000994316

10%

40%

50%

0.009448508

0.001078417

10%

45%

45%

0.008963154

0.001048829

10%

50%

40%

0.008477799

0.001020796

0%

100%

0%

0.000113586

0.000863006

0%

0%

100%

0.009820684

0.001410312

0%

5%

95%

0.009335329

0.001368184

0%

95%

5%

0.000598941

0.000875609

0%

10%

90%

0.008849974

0.001327611

0%

90%

10%

0.001084296

0.000889766

0%

15%

85%

0.00836462

0.001288591

0%

85%

15%

0.001569651

0.000905477

0%

80%

20%

0.002055005

0.000922742

0%

20%

80%

0.007879265

0.001251125

0%

25%

75%

0.00739391

0.001215213

0%

75%

25%

0.00254036

0.000941561

0%

30%

70%

0.006908555

0.001180855

0%

70%

30%

0.003025715

0.000961933

0%

35%

65%

0.0064232

0.001148051

0%

65%

35%

0.00351107

0.00098386

0%

40%

60%

0.005937845

0.001116801

0%

60%

40%

0.003996425

0.00100734

0%

45%

55%

0.00545249

0.001087105

0%

55%

45%

0.00448178

0.001032375

 

 

 

 

 

 

 

 

 

 

 

版权归属essaylunwen.com邦典论文网,严谨转载,违者必究!

点击次数:  更新时间:2014-08-31  【打印此页】  【关闭