Financial Market Analysis

Financial Market Analysis

The geometric mean and the arithmetic mean Returns and standard deviations over time.

(%) Arithmetic Mean

Geographic Mean (%)

Standard Deviation (%)

Large-capitalization stocks in the United States

8.393333333

7.918495681 18.1682009 Small Cap, Stocks in the United States

Inv. Grade USD Bonds 10.63333333 8.487053338 21.63068808

4.606666667\s4.872027764\s2.998920441

Real Estate Trusts in the United States

12.84

10.79335882\s20.45667198\sCommodities

2.993333333\s1.15890429

19.13995323

Stocks in Development 8.026666667 5.745468597

Emerging Market Equities 21.21880792 14.76666667 9.8427609

USD Bonds of Certain Grade 32.64665082

10.60666667\s9.277849696\s18.6968854

From the results depicting the Arithmetic and geometric means of the historical rates of return for the asset classes, there is closeness in the values. This phenomenon implies that the performance of the assets is a true reflection of the portfolio performance. However, US Small Cap., Equities, Dev. Econ. Equities and Emerging Mkt. Equities have larger standard deviations (%), implying that the Arithmetic means of these asset classes overstate the actual portfolio performance. Thus, their geometric means draw the actual reflection of their performance (Bodie et al. 345).

Correlation matrix

US Large Cap. Equities

US Small Cap, Equities

Inv. Grade USD Bonds

US Real Estate Trusts

Commodities

Dev. Econ. Equities

Emerging Mkt. Equities

Spec. Grade USD Bonds

US Large Cap. Equities

1.0000

0.9413

-0.4325

0.7134

0.3401

0.8888

0.6872

0.7185

US Small Cap, Equities

0.9413

1.0000

-0.4339

0.7147

0.4339

0.8767

0.6734

0.7225

Inv. Grade USD Bonds

-0.4325

-0.4339

1.0000

-0.0068

0.2904

-0.3381

0.0212

0.0298

US Real Estate Trusts

0.7134

0.7147

-0.0068

1.0000

0.4585

0.7254

0.6368

0.6919

Commodities

0.3401

0.4339

0.2904

0.4585

1.0000

0.5641

0.7655

0.6216

Dev. Econ. Equities

0.8888

0.8767

-0.3381

0.7254

0.5641

1.0000

0.8687

0.7879

Emerging Mkt. Equities

0.6872

0.6734

0.0212

0.6368

0.7655

0.8687

1.0000

0.8655

Spec. Grade USD Bonds

0.7185

0.7225

0.0298

0.6919

0.6216

0.7879

0.8655

1.0000

The correlation coefficients of 0.7 and above indicate that the returns of the portfolio assets move in together and are statistically significant. On the other hand, the correlation coefficients of 0.3 and below indicate that the returns on the respective portfolio are not statistically significant and as such, investment on such assets incurs higher risks than is necessary. Lastly, the negative coefficients imply that the average returns on the asset classes move in opposite directions (Poon, Ser-Huang 45).

Covariance matrix and boarder-multiplied covariance matrix for an equally weighted portfolio

Covariance matrix

US Large Cap. Equities

US Small Cap, Equities

Inv. Grade USD Bonds

US Real Estate Trusts

Commodities

Dev. Econ. Equities

Emerging Mkt. Equities

Spec. Grade USD Bonds

US Large Cap. Equities

330.0835

369.9295

-23.5635

265.1560

118.2521

342.6295

407.6069

244.0572

US Small Cap, Equities

369.9295

467.8867

-28.1488

316.2507

179.6502

402.3812

475.5490

292.2126

Inv. Grade USD Bonds

-23.5635

-28.1488

8.9935

-0.4181

16.6715

-21.5145

2.0795

1.6692

US Real Estate Trusts

265.1560

316.2507

-0.4181

418.4754

179.5253

314.8739

425.3043

264.6526

Commodities

118.2521

179.6502

16.6715

179.5253

366.3378

229.0895

478.3140

222.4508

Dev. Econ. Equities

342.6295

402.3812

-21.5145

314.8739

229.0895

450.2378

601.7545

312.5998

Emerging Mkt. Equities

407.6069

475.5490

2.0795

425.3043

478.3140

601.7545

1065.8038

528.2867

Spec. Grade USD Bonds

244.0572

292.2126

1.6692

264.6526

222.4508

312.5998

528.2867

349.5735

Boarder-multiplied Covariance matrix

US Large Cap. Equities

US Small Cap, Equities

Inv. Grade USD Bonds

US Real Estate Trusts

Commodities

Dev. Econ. Equities

Emerging Mkt. Equities

Spec. Grade USD Bonds

(weight)

0.125

0.125

0.125

0.125

0.125

0.125

0.125

0.125

US Large Cap. Equities

0.1250

5.1576

5.7801

-0.3682

4.1431

1.8477

5.3536

6.3689

3.8134

US Small Cap, Equities

0.1250

5.7801

7.3107

-0.4398

4.9414

2.8070

6.2872

7.4305

4.5658

Inv. Grade USD Bonds

0.1250

-0.3682

-0.4398

0.1405

-0.0065

0.2605

-0.3362

0.0325

0.0261

US Real Estate Trusts

0.1250

4.1431

4.9414

-0.0065

6.5387

2.8051

4.9199

6.6454

4.1352

Commodities

0.1250

1.8477

2.8070

0.2605

2.8051

5.7240

3.5795

7.4737

3.4758

Dev. Econ. Equities

0.1250

5.3536

6.2872

-0.3362

4.9199

3.5795

7.0350

9.4024

4.8844

Emerging Mkt. Equities

0.1250

6.3689

7.4305

0.0325

6.6454

7.4737

9.4024

16.6532

8.2545

Spec. Grade USD Bonds

0.1250

3.8134

4.5658

0.0261

4.1352

3.4758

4.8844

8.2545

5.4621

1.0000

32.0961

38.6830

-0.6911

34.1222

27.9733

41.1258

62.2609

34.6172

Portfolio Variance

235.5702009

Portfolio SD

15.34829635

15.34829635

Portfolio Arithmetic Mean

9.108333333

Portfolio Geometric Mean

7.261989886

Work cited

Bodie, Zvi. Investments. McGraw-Hill, 2013. 345-368

Poon, Ser-Huang. A practical guide to forecasting financial market volatility. John Wiley & Sons, 2005