This study presents the application of portfolio direction theoretical accounts and theories in the allotment of assets and choice of portfolio securities. It gives a elaborate description of the analytical procedure involved in setting-up a portfolio composed of six mostly traded market indices denominated in USD. The optimum assets allocation scheme was based on a clip series informations of monthly entire return of the selected market indices from 31st Dec 1996 to 30th Sep 2009.

The study is divided into three subdivisions ; in Section-A, we present an analysis of different portfolio plus allotment and choice standards based on the Harry Markowitz portfolio optimization theoretical account utilizing an false in-sample informations of the indices ‘ entire return from 31st Dec. 1996 – 31st Dec. 2001 ( in-sample period ) . Section-B nowadayss the out-sample public presentation of the different portfolio plus allotment standards analysed in subdivision A. In Section-C, we attempt to analyze the risk-return public presentation of the Harvard Endowment fund utilizing the highlighted portfolio choice standards in Section A and B.

## Section A.

## Portfolio Assets Allocation Criteria – In Sample Data

We analysed different assets allotment schemes for a portfolio of six good traded market indices that includes the S & A ; P-500 Index ( “ S & A ; P ” ) , Dow Jones Corporate Bond Total Index ( “ Dow ” ) , MSCI BRIC Standard ( Gross ) Index ( “ MSCI-BRIC ” ) , Dow Jones-UBS Commodity Index ( “ UBS ” ) , MSCI EAFE ( Gross ) Index ( “ MSCI-EAFE ” ) and the HFRI Fund of Funds Composite Index ( “ HFRI ” ) .

We analysed the risk-return behavior of the market indices over the in-sample period to find the portfolio allotment weights for a Minimum-Variance and Tangent Portfolios. Our theoretical account is based on the Harry Markowitz portfolio optimisation theory, which states that the optimum allotment scheme that minimises entire portfolio hazard for a given degree of return or maximises entire return for a given degree of hazard.

The application of this thought consequences into a list efficient portfolios that lie along the efficient frontier generated as a solution to multi nonsubjective LP. Mathematically a portfolio can be represented as a vector, where is the sum ( in fraction ) of plus allocated into an investing.

The entire portfolio return is, where is the figure of securities in the portfolio.

The associated portfolio hazard ( for a two assets portfolio ) is given as ;

## .

Markowitz argued that this entire portfolio hazard will ever be less than the amount of the component assets ‘ hazards as a consequence of the variegation effects on the portfolio when the returns of the securities are non absolutely positively correlated.

The risk-return behavior of the market indices and their co-variances based on the in-sample informations period are presented in the tabular array below:

## Covariance Matrix

## A

## S & A ; P

## Dow

## MSCI

## UBS

## EAFE

## HFRI

## S & A ; P

## 0.26 %

## 0.01 %

## 0.33 %

## 0.03 %

## 0.19 %

## 0.06 %

## Dow

0.01 %

## 0.02 %

0.00 %

0.00 %

0.00 %

0.00 %

## MSCI

0.33 %

0.00 %

## 1.10 %

0.11 %

0.31 %

0.17 %

## UBS

0.03 %

0.00 %

0.11 %

## 0.17 %

0.03 %

0.02 %

## EAFE

0.19 %

0.00 %

0.31 %

0.03 %

## 0.22 %

0.06 %

## HFRI

0.06 %

0.00 %

0.17 %

0.02 %

0.06 %

## 0.05 %

Average Tax return

0.87 %

0.61 %

0.40 %

-0.03 %

0.21 %

0.69 %

## Optimal Tangent portfolio

The portfolio aim of understating hazard and maximizing return outputs an efficient frontier of different portfolios each of which is optimum for a different value of risk-return. An investor chooses a suited portfolio on the efficient frontier depending on his hazard position.

The optimum tangent portfolio is the portfolio that maximises the extra return over hazard free rate per unit of hazard. This is measured with the Sharpe ratio: .

In gauging the tangent portfolio, we determined the portfolio allotment weights that maximises the Sharpe ratio. In this calculation we have taken risk free rate of return to be 0.487 % per month ( 6 % -per annum ) . This was obtained from the US-Treasury rates records for the in-sample period.

The tabular array below present the optimum tangent portfolio allotment weights among the six market indices.

Tangent Portfolio

Required return

## S & A ; P

## Dow

## MSCI

## UBS

## EAFE

## HFRI

## Entire

## Weight

## 2.10 %

## 64.95 %

## 0.00 %

## 0.00 %

## 0.00 %

## 32.96 %

## 100 %

Expected Tax return

0.641 %

Risk Free Return

Assumed

6 % p/a

0.487 %

Discrepancy

0.014 %

Standard divergence

1.179 %

Max Sharpe ratio

Optimised with excel convergent thinker

## A

## A

13.05 % A

The graphs below comparison the comparative places of each market index to the efficient frontier and the tangent portfolio.

As indicated on the efficient frontier, the Tangent portfolio posts a superior public presentation compared to the single market indices. This is farther analysed in the tabular array below. The Sharpe ratios of the efficient frontier portfolios are depicted in the Sharpe ratio curve. This shows that the ratio is maximised at the return of 0.614 % , the return of the tangent portfolio.

## Asset

Tax return

Hazard

Sharpe

## S & A ; P

0.87 %

5.12 %

7.40 %

## Dow

0.61 %

1.24 %

9.67 %

## MSCI

0.40 %

10.47 %

-0.87 %

## UBS

-0.03 %

4.17 %

-12.47 %

## EAFE

0.21 %

4.69 %

-5.94 %

## HFRI

0.69 %

2.22 %

9.32 %

## Portfolio

0.641 %

1.179 %

13.05 %

## Minimum-Variance Portfolio

The minimal discrepancy portfolio is the portfolio on the efficient frontier with the minimal degree of hazard. This is the portfolio for the hazard averse investor. It guarantees the least sum of hazard for puting in a portfolio incorporating a combination of the six market indices.

The tabular array below presents the optimum plus allotment weights to accomplish a minimal discrepancy portfolio:

Minimal Discrepancy

## A

## S & A ; P

## Dow

## MSCI

## UBS

## EAFE

## HFRI

## Entire

## Weight

## 0.00 %

## 76.62 %

## 0.00 %

## 2.39 %

## 0.00 %

## 20.99 %

## 100 %

Expected Tax return

0.609 %

Discrepancy

0.012 %

Standard divergence

## A

## A

## A

## A

## A

1.106 %

## Section B.

## Out-sample Portfolio Performance

Our optimum tangent and minimum-variance portfolio weights based on the in-sample information was tested on the portfolio over the out-of-sample period from 31st Dec. 2001 – 30th Sep. 2009. We assumed a monthly portfolio rebalancing based on each of the allotment schemes. Our findings for the Tangent and Minimum Variance Portfolio are presented in the tabular array below:

Tangent Portfolio

Required return

## S & A ; P

## Dow

## MSCI

## UBS

## EAFE

## HFRI

## Entire

Weight

2.10 %

64.95 %

0.00 %

0.00 %

0.00 %

32.96 %

100 %

Monthly Mean Return

0.503 %

Risk Free Return

Assumed

6 % p/a

0.487 %

Monthly Discrepancy

0.027 %

Monthly Standard divergence

## A

## A

## A

## A

1.637 %

Average Monthly Portfolio Turnover ( ( As a % of portfolio value )

0.39 %

Minimal Discrepancy

## A

## S & A ; P

## Dow

## MSCI

## UBS

## EAFE

## HFRI

## Entire

Weight

0.00 %

76.62 %

0.00 %

2.39 %

0.00 %

20.99 %

100 %

Monthly Mean Return

0.549 %

Monthly Discrepancy

0.031 %

Monthly Standard divergence

## A

## A

## A

## A

## A

## A

1.767 %

Average Monthly Portfolio Employee turnover

( As a % of portfolio value )

0.33 %

As shown in the tabular arraies above, the minimal discrepancy portfolio ‘s public presentation is superior to the tangent portfolio both in returns and mean monthly turnover. The lower monthly turnover for the minimal discrepancy indicates that the portfolio will incur a lower sum of dealing costs in purchasing and selling component assets in order to rebalance the portfolio on a monthly footing. This individual fact may account for the superior return posted by the minimal discrepancy portfolio.

However, when the consequences of these two portfolios are juxtaposed with an every bit leaden portfolio, it indicates an wholly different scenario. The every bit leaden portfolio was superior to these portfolios at both average return and crisp ratio degrees. This consequence supports the place of the every bit leaden optimum portfolio theory. This theory is based on the fact that no portfolio allotment scheme will surpass a moderately rebalanced every bit leaden portfolio allotment portfolio scheme. The public presentation of an every bit leaden portfolio over the out-of-sample period is presented in the tabular array below:

## Equally Weighted Portfolio

Required return

## S & A ; P

## Dow

## MSCI

## UBS

## EAFE

## HFRI

## Entire

Weight

16.67 %

16.67 %

16.67 %

16.67 %

16.67 %

16.67 %

100 %

Monthly Mean Return

0.753 %

Monthly Discrepancy

0.142 %

Monthly Standard divergence

## A

## A

## A

## A

## A

3.767 %

Average Monthly Portfolio Employee turnover

( As a % of portfolio value )

1.29 %

The following tabular array compares the Sharpe ratios of the three portfolio allotment scheme, and it one time once more proves the high quality of the every bit leaden portfolio over the tangent and the minimal discrepancy portfolio.

Scheme

Sharpe Ratio

Minimal Discrepancy

3.53 %

Tangent Portfolio

1.02 %

Equally leaden Portfolio

7.08 %

## Harvard Endowment Fund Risk Report

Harvard Endowment fund is the universe ‘s largest gift fund owned by a university. In this subdivision we present a hazard analysis of the US $ 26 billion deserving gift fund.

In transporting out this analysis, we have assumed a re-adjusted allotment expression in order to augment the deficit in the adjusted expression provided in the job. Our plus allotment expression was arrived at with full consideration for the gift fund investing standards. The current value of the fund was allocated among the six market indices under survey as shown in the graph below ;

The public presentation of the fund was measured based on the entire return informations of the six market indices from 31st Dec. 1996 to 30th Sep. 2009. The risk-return matrix of the constituent indices as at 30th Sep. 2009 is presented in the tabular array below:

## Risk-Return Matrix

## A

## S & A ; P

## Dow

## MSCI

## UBS

## EAFE

## HFRI

## Cash

## S & A ; P

## 0.23 %

0.02 %

0.30 %

0.06 %

0.20 %

0.05 %

0.00 %

## Dow

0.02 %

## 0.03 %

0.04 %

0.01 %

0.03 %

0.01 %

0.00 %

## MSCI

0.30 %

0.04 %

## 0.88 %

0.19 %

0.36 %

0.13 %

0.00 %

## UBS

0.06 %

0.01 %

0.19 %

## 0.24 %

0.10 %

0.04 %

0.00 %

## EAFE

0.20 %

0.03 %

0.36 %

0.10 %

## 0.26 %

0.06 %

0.00 %

## HFRI

0.05 %

0.01 %

0.13 %

0.04 %

0.06 %

## 0.04 %

## 0.00 %

## Cash

0.00 %

0.00 %

0.00 %

0.00 %

0.00 %

0.00 %

0.00 %

Expected Tax return

Average

0.33 %

0.60 %

1.39 %

0.42 %

0.49 %

0.47 %

0.49 %

The hazard return prosodies of the fund based on the fund based on the stated allotment scheme is presented in the tabular array below:

Harvard current portfolio Risk-Return Prosodies

## A

## S & A ; P

## Dow

## MSCI

## UBS

## EAFE

## HFRI

## Cash

## Entire

Weight

11.00 %

22.00 %

11.00 %

14.00 %

11.00 %

29.00 %

2.00 %

100 %

Expected Return ( Monthly )

0.596 %

Portfolio Value ( $ ‘billion )

26

Monthly Discrepancy

0.082 %

Monthly Standard divergence

## A

## A

## A

## A

## A

2.872 %

## Portfolio Drawdown

There has being a considerable sum of draw-downs in the value of the Harvard gift fund most particularly in the late period of 2008 and the early times of 2009. The portfolio grew significantly between 2003 and 2007 and experienced a really deep autumn in the early portion of 2009. The highest value the fund has reached was US $ 30.26 billion on 31st Oct. 2007 and the lowest value in the recent clip was US $ 20.1 billion on 27th Feb. 2009. The undermentioned graph depicts the draw-downs experienced by the fund since 1996 to day of the month.

## Value At Risk ( VaR )

We computed a 99 % monthly VaR for the Harvard portfolio utilizing the historical method. The gift fund ‘s VaR as at 30th Sep. 2009 is US $ 2.49 billion. This was derived by taking the 99th percentile of the past 153 monthly norm portfolio returns covering the period from 31st Dec. 1996 – 30th Sep. 2009. This means that the fund should put aside an sum of US $ 2.49 billion in fund capital and be rest assured with 99 % assurance that a loss of this sum of money can merely be exceeded 1 % in 153 months.

A Loss ( $ ‘billion )

1

– 3.43

2

– 2.54

3

– 2.45

4

– 1.26

5

– 1.11

6

– 1.02

7

– 0.94

8

– 0.94

9

– 0.92

10

– 0.85

The short-coming of the computed VaR is that is has to be updated from clip to clip ( monthly in this instance ) in order to take into consideration freshly happening utmost events.

## Correlation Analysis

A correlativity analysis of the portfolio constituent market indices is presented in the tabular array below:

## Correlational Analysis Matrix

## A

## S & A ; P

## Dow

## MSCI

## UBS

## EAFE

## HFRI

## S & A ; P

## 1.00

0.25

0.67

0.24

0.84

0.58

## Dow

0.25

## 1.00

0.23

0.16

0.30

0.19

## MSCI

0.67

0.23

## 1.00

0.43

0.76

0.76

## UBS

0.24

0.16

0.43

## 1.00

0.38

0.44

## EAFE

0.84

0.30

0.76

0.38

## 1.00

0.65

## HFRI

0.58

0.19

0.76

0.44

0.65

## 1.00

This tables shows that the returns of the six market indices are partly positively correlated. This therefore limits the full effects of portfolio variegation on the public presentation of the hazard of the gift fund.