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© 2012 Morningstar, Inc. All rights reserved. The information in this document is the property of Morningstar, Inc. Reproduction or transcription

by any means, in whole or part, without the prior written consent of Morningstar, Inc., is prohibited.

1

Morningstar X-Ray Tool Methodology Guide v2.1

Introduction .................................................................................................................................. 2

Grouping X-Ray’s Calculations: Portfolio or NAV Based ............................................................ 3

Portfolio Based Statistics .............................................................................................................. 4

Asset Class Composition .......................................................................................................... 4

Top 10 Country Breakdown ...................................................................................................... 8

Equity Style Exposure ............................................................................................................. 10

Fixed-Income Style Exposure ................................................................................................. 13

Equity Sector Breakdown ....................................................................................................... 16

Regional Exposure .................................................................................................................. 19

Top 10 Holdings ..................................................................................................................... 22

Top 10 Underlying Holdings .................................................................................................... 23

Equity Portfolio Statistics ....................................................................................................... 26

Fixed-Income Portfolio Statistics ............................................................................................ 29

Holding Overlap ...................................................................................................................... 32

NAV Based Statistics ................................................................................................................. 35

Performance .......................................................................................................................... 35

Investment Growth Graph ...................................................................................................... 38

Risk / Reward Scatter Plot ..................................................................................................... 41

Correlation Matrix .................................................................................................................. 42

Appendix A: Sample X-Ray PDF Report ...................................................................................... 43



2

Introduction

The purpose of Morningstar’s X-Ray tool is to analyze an investor’s portfolio of investment holdings.

The X-Ray’s principal result is transparency. For instance, with the X-Ray an investor can find out the

proportions of total assets that are invested in different sectors, regions, equity styles or countries.

The investor can also find out if he or she is indirectly exposed to the same stock in different funds,

the amount of assets invested in a particular stock or the portfolio’s fundamental ratios. The X-Ray

is meant to be used when the investor has at least two holdings for analysis. For single holding

analysis, Morningstar’s Investment Detail report is more suitable.

The following definitions are used extensively in this document:

� Investor’s Portfolio = The portfolio of an X-Ray user or advisor

� Holding = A holding in an investor’s portfolio. In general, a holding can be any type of

security (e.g. open end fund, stock or bond)

The X-Ray is available in both HTML and PDF output. These differ slightly in that the HTML version is

interactive (allows more detail in various pages) and the PDF version is both, and usually more

visually compelling. This document is written to cover all functions in both outputs as there is

significant overlap, however, you may see the diagrams and figures differ slightly depending on

which is being viewed. The view will be indicated where applicable.



3

Grouping X-Ray’s Calculations: Portfolio or NAV Based

One can think of an X-Ray report as having sections belonging to two groups. The first group

contains all sections where the statistics are based on holdings’ portfolios. The second group

contains all sections where the statistics are based on holdings’ NAVs. In an X-Ray report the

following sections may appear:

Portfolio Based

� Asset Class Composition

� Top 10 Country Breakdown

� Equity Style Exposure

� Fixed-Income Style Exposure

� Equity Sector Weightings

� Regional Exposure

� Top 10 Holdings

� Top 10 Underlying Holdings

� Equity Portfolio Statistics

� Fixed-Income Portfolio Statistics

� Holding Overlap

NAV Based

� Performance

� Investment Growth Graph

� Risk / Reward Scatter Plot

� Correlation Matrix

© 2012 Morningstar, Inc. All rights reserved. The information in this document is the property of Morningstar, Inc. Reproduction or transcription by any

means, in whole or part, without the prior written consent of Morningstar, Inc., is prohibited.

4

Portfolio Based Statistics

Asset Class Composition

The broad asset class allocation gives an impression of how the investor’s portfolio is distributed over

different asset classes. An example of this can be seen in Figure 1.a. The asset class lineup can also be

customized based on the data available for classifying holdings in Morningstar’s database.

Figure 1.a

Morningstar distinguishes between the broad asset classes, see below for an example:

Asset class Description

Cash Sum of all cash holdings

Equity Sum of all equity holdings

Bond Sum of all bond holdings

Property Sum of all property holdings



5

Other Sum of all holdings in derivatives and receivables

Not classified Sum of all holdings that could not be classified in any of the above

Since a holding’s exposure to a particular broad asset class can vary and the investor has the possibility

to invest and divest in a holding daily, the X-Ray must first calculate the investor’s weight in a holding

before calculating exposure to an asset class.

Morningstar will calculate both long and short breakdowns for asset allocation. The percent in each asset

class is the total long or short market value in that asset class divided by the total market value in the

portfolio.

The long percentages will always represent positive numbers and the short percentages will always

represent negative numbers. These won’t necessarily add up to 100% independently.

If there are no short positions or derivatives in the portfolio, the long asset allocation breakdown will add

up to 100%. If there are short positions and these are fully collateralized, the long positions will typically

add up to more than 100%.

Net asset allocation is calculated by adding together the long and short position.

The investor’s current assets in a fund i at time t is determined by the number of shares and the value of

each share. At time t, the value of the investment in fund i is:

itiit navshcv *=

where:

si = Number of shares of fund i

navit = The latest NAV for fund i

The total value of the investor’s combined holdings is:

∑=

n

i

ithcv1

where:



6

n = Number of holdings in the user portfolio

Consequently, the investor’s weight in holding i at time t is:

∑=

=n

i

it

itit

hcv

hcvw

1

Using each holding’s weight, one can calculate the investor’s cash exposure as follows:

∑=

=

n

i

iti whpcppc1

*

where:

ppc = The investor’s percentage cash exposure

hpci = Cash percentage in fund i

n = Number of holdings in investor’s portfolio

Using the same methodology, one can calculate the investor’s equity, bond, other and “not classified”

exposure.

∑=

=

n

i

iti whpeppe1

*

∑=

=

n

i

iti whpbppb1

*

∑=

=

n

i

iti whpoppo1

*

∑=

=

n

i

iti whpncppnc1

*

Note that a holding or fund’s investment in an asset class is estimated using the fund’s portfolio of

securities. The portfolio’s date might be different from time t, when the X-Ray is produced. Since



7

portfolios are normally updated frequently, the X-Ray’s broad asset class composition statistics will

usually be current in general.

Also note that the broad asset class allocation percentages sum to 100%.



8

Top 10 Country Breakdown

The Top 10 Country Breakdown gives the distribution of the investor’s assets across different countries.

Morningstar’s databases contain all countries. Figure 1.b shows an example of this breakdown:

Figure 1.b

An investor’s exposure to a country is determined by how much money is invested in a holding and the

amount of money in that holding invested in a particular country’s companies. Note that the X-Ray only

uses a holding’s equity portion when it calculates the breakdown by country. Bond holdings are excluded.

An investor might be exposed to a country by being invested in fixed-income securities issued in a

particular country.

At any time t, the value of an investor’s assets in holding i is:

itiit navshcv *=

where:

si = Number of shares of fund i


A holding may or may not be invested in equity / companies. The value of assets in fund i exposed to

equity is:

iit hpshcv *

where:

hpsi = Percent of equity in holding i



9

Given each holding’s value exposure to equity, the X-Ray calculates each holding’s equity weight as:

∑=

=n

i

iit

iit

it

hpshcv

hpshcvw

1

*

*

where:


Using these holding weights, it is possible to estimate the investor’s distribution of current assets across

countries. Per country, the allocation is calculated as follows:

∑=

=

n

i

iti whcpc1

*

where:

pc = The country exposure in an investor’s portfolio

hci = The percentage of holding i that is invested in a country

wit = Weight of holding i in investor’s portfolio at time t

To get the top ten countries, the X-Ray ranks the countries in descending order and then selects the top

ten countries. These are represented in the X-Ray report.

Also note that the top ten country exposure statistics are based on each holding’s portfolio of securities.

The portfolio’s date might be different than time t, when the X-Ray is produced. If the investment

objective of the fund does not vary often, the country exposure for the fund should remain fairly stable.

Finally, note that the top ten country holding percentages may not sum to 100 percent since the table

may not include the investor’s country exposures past the top ten.



10

Equity Style Exposure

The equity style exposure gives an impression of how the investor’s assets are distributed across

Morningstar’s nine different equity style categories, as shown in Figure 1.d and 1.e.

Figure 1.c

Figure 1.d



11

Note that it is only a holding’s equity portion that is considered in the calculation. Bond holdings are

excluded.

An investor’s equity style exposure is determined by how much money is invested in the holding, the

percentage invested in equity and the corresponding equity style distribution.

At any time t, the value of an investor’s assets in fund i is:

itiit navshcv *=

where:

si = Number of shares of mutual fund i


A holding may or may not be fully invested in equity. The value of assets in fund i exposed to equity is:

iit hpshcv *

where:


Given each holding’s exposure to equity, the X-Ray can calculate each holding’s equity weight as:

∑=

=n

i

iit

iit

it

hpshcv

hpshcvw

1

*

*

where:


The X-Ray can now calculate an investor’s overall equity style exposure by summing each holding’s

exposure to a particular style.

∑=

=

n

i

iti whlspes1

*



12

where:

pes = The percentage of the equity style in the investor’s portfolio

hls = The percentage of the equity style in holding i



13

Fixed-Income Style Exposure

The underlying idea behind the fixed-income style box is similar to the equity style box. By looking at the

fixed-income style box an investor gets a snapshot of the quality and the risk associated with a portfolio

of bond funds. See Figure 1.e and 1.f for how this information is presented.

Figure 1.e

Figure 1.f

Since Morningstar does not collect a bond fund’s complete portfolio holdings, the X-Ray cannot calculate

a single fund’s splits in the fixed-income style box. Instead, a bond fund’s style box will always be

allocated to a single style (e.g. 100% allocated to high quality / short duration). If an X-Ray user has many



14

bond funds in his X-Ray, the fixed-income style box will show the weighted style exposures of the

investor’s holdings. In Figure 1.e above, Morningstar’s fixed-income style categories can be seen.

The information regarding fixed-income funds’ holdings comes from the bond fund summaries collected

by Morningstar. These summaries are inquiries and not exhaustive surveys of funds’ holdings.

Note that the fixed-income style exposure only considers bond funds that have bond summaries. An

investor’s exposure to a bond holding’s style is determined by how much money is invested in the

holding and the holding’s style distribution.

At any time t, the value of an investor’s assets in bond fund i is:

itiit navshcv *=

where:

si = Number of shares of bond fund i


The total value of the investor’s combined bond holdings is:

∑=

n

i

ithcv1

where:


Consequently, the investor’s weight in bond holding i at time t is:

∑=

=n

i

it

it

it

hcv

hcvw

1

The X-Ray can now calculate an investor’s overall fixed-income style exposure by summing each

holding’s exposure to a particular fixed-income style.

iti wfisbfisb *=



15

where:

fisb = The weighted fixed-income style box percentage exposure

fisbi = The fixed-income style box of bond fund i



16

Equity Sector Breakdown

The sector weightings allocation shows the distribution of an investor’s assets across different stock

sectors.

Figure 1.g

Figure 1.h

There are three main sectors, with eleven sub divisions, as seen above in Figure 1.g and 1.h.

Morningstar estimates a fund’s exposure to sectors by linking each equity holding in the fund’s portfolio

to a Morningstar sector. This produces a sector distribution for each fund.



17

An investor’s exposure to a fund holding’s sector distribution is determined by how much money is

invested in the holding, how much of that money is invested in equity and how the equity money is

distributed over companies classified into different sectors.


itiit navshcv *=

where:



A holding may or may not be invested in equity. The value of assets in fund i exposed to equity is:

iit hpshcv *

where:



∑=

=n

i

iit

iit

it

hpshcv

hpshcvw

1

*

*

where:


Using these weights, the X-Ray estimates the investor’s distribution of current assets across different

sectors.

Per sector, the allocation is calculated as follows:

∑=

=

n

i

iti whsps1

*



18

where:

ps = The percentage of a sector in the investor’s portfolio

hsi = The percentage of holding i that is invested in a sector


Note that sector allocations are only estimated for equity holdings. Bond fund’s that invest in corporate

debt, for example, are excluded from these calculations.



19

Regional Exposure

This segment provides a broad breakdown of a portfolio’s geographical exposure based on the

percentage weight of the investment within the portfolio relevant to the percent of security that equals

equity. Only non-cash equity assets are evaluated in determining the exposures. ‘Not Classified’

indicates the percentage of the equity portion of the portfolio for which Morningstar is unable to assess

region or origin. The regional categories and general layout can be seen in Figure 1.i and 1.j below:

Figure 1.i

Figure 1.j

Note that combination of all regions covers the whole world. Also note that regions can encompass

more than one country.




20

itiit navshcv *=

where:



A holding may or may not be invested in equity. The value of assets in fund i exposed to equity is:

iit hpshcv *

where:



∑=

=n

i

iit

iit

it

hpshcv

hpshcvw

1

*

*

where:


Using these weights, the X-Ray estimates the investor’s distribution of current assets across different

world regions.

Per sector, the allocation is calculated as follows:

∑=

=

n

i

iti whrpr1

*

where:

pr = The percentage of a region in the investor’s portfolio

hri = The percentage of holding i that is invested in a region




21

Note that sector allocations are only estimated for equity holdings. All other holdings of a fund are

excluded from these calculations.



22

Top 10 Holdings

The Top 10 Holdings list gives a snapshot of the investor’s ten largest holdings within his portfolio. The

holdings are ranked based on each holding’s weight in the portfolio as can be seen in Figure 1.k.

Figure 1.k

At any time t, the value of an investor’s assets in fund / holding i is:

itiit navshcv *=

where:



Given values for all holdings, a holding’s weight is calculated as follows:

∑=

=n

i

it

it

it

hcv

hcvw

1

where:

wi = Weight of holding i in user portfolio


These holding weights are ranked in descending order, whereupon the top ten holdings are selected and

listed as ‘Top 10 Holdings’.

Note that a holding is normally a fund, not a share in a company.



23

Top 10 Underlying Holdings

The Top 10 Underlying Holdings list is different from the Top 10 Holdings list. Whereas the latter is

concerned about securities directly owned by the investor, the former is concerned about securities

indirectly owned by the investor (normally funds’ holdings). An example of this can be seen in Figure 1.l

below.

Figure 1.l

An investor’s indirect ownership in a company depends on how much money is invested in equity funds

and how much of the equity funds’ assets are invested in the company. To calculate this, one must first

calculate the investor’s assets in different funds, how much of it is invested in equity and how much of

this equity money is invested in a specific company.


itiit navshcv *=

where:




equity is:



24

iit hpshcv *

where:



∑=

=n

i

iit

iit

it

hpshcv

hpshcvw

1

*

*

where:

n = Number of holdings in the investor’s portfolio

Using these holding weights, it is possible to calculate the investor’s distribution of current assets across

companies. Per company, the allocation is calculated as follows:

∑=

=

n

i

iti whccpcc1

*

where:

pcc = The company exposure in an investor’s portfolio

hcci = The percentage of holding i that is invested in a company


To get the top ten, the X-Ray ranks the companies in descending order and then selects the top ten

underlying holdings. Their percentages, as well as the amount of money invested in each underlying

holding, are printed in the X-Ray report.

Note that only equity holdings are used to calculate this top ten. Bond holdings are excluded. An investor

might be exposed to a company by having invested in fixed income securities issued by the company.

Also note that the Top 10 Underlying Holdings rankings are based on each holding’s portfolio of

securities. The portfolio’s date might be different than time t. If a fund’s underlying holdings have

changed, the top ten will be less accurate.



25

Finally, note that the Top 10 Underlying Holdings’ percentages may not sum to 100 percent since an

investor’s exposure to the companies outside of the top ten are excluded.



26

Equity Portfolio Statistics

The equity portfolio statistics give the investor his portfolio’s fundamental ratios, as well as the average

ratios of the funds’ underlying holdings, as can be seen in Figure 1.m below.

Figure 1.m

Morningstar’s stock database contains nearly all companies listed on different markets in the world. For

each company, Morningstar receives a monthly data-feed of the company’s price / earnings (P/E), price /

cash flow from continuing operations (P/CF) and price / book value (P/B). The ratios are used when

analyzing the value of a company’s earnings, cash flows and assets.


itiit navshcv *=

where:



A holding may or may not be fully invested in equity. The value of assets in fund i exposed to equity is:

iit hpshcv *

where:


Given each holding’s value exposure to equity, the X-Ray can calculate each holding’s equity weight as:



27

∑=

=n

i

iit

iit

it

hpshcv

hpshcvw

1

*

*

where:


The X-Ray calculates an investor’s weighted equity portfolio ratios by summing each holding’s weighted

P/E, P/CF, P/PB ratios and median market cap.

∑=

=

n

i

itit whpeppe1

*

where:

ppet = The P/E ratio of the investor’s portfolio at time t

hpei = The P/E ratio of holding i

∑=

=

n

i

itit whcfpcf1

*

where:

pcft = The P/CF ratio of the investor’s portfolio at time t

hcfi = The P/CF ratio of holding i

∑=

=

n

i

itit whpbppb1

*

where:

ppbt = The P/B ratio of the investor’s portfolio at time t

hpbi = The P/B ratio of holding i

∑=

=

n

i

itit whmmcpmmc1

*

where:



28

pmmct = The median market capitalization of the investor’s portfolio at time t

hmmci = The median market capitalization of holding i



29

Fixed-Income Portfolio Statistics

The fixed-income portfolio statistics are calculated in exactly the same manner as the equity portfolio

statistics. Instead of P/E, P/CF, P/B and median market cap, the fixed-income statistics are effective

duration, effective maturity and credit quality. Figure 1.n below shows an example of this data and its

layout.

Figure 1.n

The information regarding fixed-income funds’ holdings comes from the bond fund summaries that

Morningstar collects from fund companies. The bond fund summaries are inquiries and not exhaustive

surveys of total holdings. In these summaries, Morningstar asks about bond funds’ effective duration,

effective maturity and credit quality.

Only fixed-income funds are included in these statistics.

At any time t, the value of an investor’s assets in bond fund i is:

itiit navshcv *=

where:

si = Number of shares of bond fund i


The total value of the investor’s combined bond holdings is:

∑=

n

i

ithcv1



30

where:


Consequently, the investor’s weight in bond holding i at time t is:

∑=

=n

i

it

it

it

hcv

hcvw

1

The X-Ray can now calculate an investor’s average effective duration, effective maturity and credit

quality by summing.

∑=

=

n

i

iti whqsdphqsd1

*

where:

pytm = Portfolio’s average yield-to-maturity

hytmi = Holding i’s yield-to-maturity

∑=

=

n

i

iti whqidphqid1

*

where:

pmd = Portfolio’s average modified duration

hmdi = Holding i’s modified duration

∑=

=

n

i

iti whcqpcq1

*

where:

pcq = Portfolio’s average credit quality

hcqi = Holding i’s credit quality



31

Morningstar classifies the contents of a fixed-income portfolio into eight subportfolios on the basis of

credit quality. For each credit quality level, there is a corresponding score (or multiplier). The score and

the bond portfolio’s percentage distribution across credit quality levels are used to calculate the average

credit quality for the overall portfolio. The credit qualities and associated scores are as follows:

Quality Score (s)

AAA/Aaa level 1

AA/Aa level 4

A level 7

BBB/Baa level 10

BB/Ba level 13

B level 16

Below B 19

Not Rated 16

A bond fund’s average credit quality is calculated by taking the bond fund’s percentage exposure to each

credit quality level weighted by each level’s score:

∑=

=

8

1 100

*

s

s sPpcq

where:

Ps = Percent of bond portfolio invested in quality level s

S = Quality levels score



32

Holding Overlap

The Holding Overlap function shows the user the ten most overlapped stocks in a given portfolio, as seen

in Figure 1.o below. For an underlying holding to be considered for the overlap calculations, it must be

invested in by at least two funds. In practice, this means the X-Ray value-ranks, in descending order, all

underlying holdings. Starting from the top, the X-Ray moves downwards and, for those underlying

holdings in which more than one fund has invested money in, a list is created. The list is the underlying

stock overlap list.

Figure 1.o



33


itiit navshcv *=

where:




equity is:

iit hpshcv *

where:



∑=

=n

i

iit

iit

it

hpshcv

hpshcvw

1

*

*

where:


Using these holding weights, it is possible to estimate the investor’s distribution of current assets across

companies. Per company, the allocation is calculated as follows:

∑=

=

n

i

iti whccpcc1

*

where:

pcc = The company exposure in an investor’s portfolio

hcci = The percentage of holding i that is invested in a company




34

To get the underlying stock overlap, the X-Ray ranks the companies in descending order and then selects

the first ten.

Note that only equity holdings are used to calculate stock overlap. Bond holdings are excluded.

The stock overlap rankings are based on each holding’s portfolio of securities. The portfolio’s date might

be different than time t. If a fund’s underlying holdings have changed, the underlying stock overlap will be

less accurate.

The most recent portfolio available for disclosure full holdings are used in this report.



35

NAV Based Statistics

Performance

This section is designed to show and compare the performance of the constituent funds being analyzed,

the collective portfolio of these funds and the appropriate benchmark.

Figure 2.a

The table to the left in Figure 2.a displays cumulative performances for the portfolio and the appropriate

benchmark, and the table to the right shows best and worst performance periods for the portfolio. Best

and Worst % are available only within the PDF report.

Figure 2.b

Figure 2.b shows the performance of each component within the X-Ray, a version of this is available in

both the PDF and HTML version.

The return figures come from Morningstar’s database. They are all based on month-end trailing

performance figures. For example, if the date is October 6, 2003 and Morningstar’s month-end

performance calculations have been run, the YTD return is based on the performance between December



36

31, 2002 and September 30, 2003. The 1-month return will be the return between August 31, 2003 and

September 30, 2003.

Note that if the date is early in a month, for example October 2, 2003, Morningstar’s month-end

calculations are still running. Since Morningstar does not publish month-end performance data until all

month-end calculations are completed, the user may get an X-Ray report with trailing performance data

which is delayed by one month plus several days. The monthly performance calculations normally are

completed around 5-6 days after every month-end.

The X-Ray month-end performance date is normally the month-end date of the underlying portfolio

holdings, however if any underlying holding in the portfolio has an earlier month-end performance date

than the rest of the holdings in the portfolio Morningstar will calculate the month-end performance

subtracting 1 month from the portfolio performance start date. This is to account for the fact that not all

funds are updated exactly at the same time during month-end data production.

Example:

Underlying Investment Latest performance date

Fund A 31/10/2011

Fund B 31/10/2011

Fund C 31/08/2011

X-Ray Start Date for the portfolio above - 30/09/2011

Underlying Investment Latest performance date

Fund A 31/10/2011

Fund B 31/10/2011

Fund C 31/10/2011

X-Ray Start Date for the portfolio above - 31/10/2011

The trailing return section also contains a row with the investor’s portfolio returns as well as a well-

known benchmark’s return (e.g. MSCI World Index).



37

The portfolio and benchmark return figures are illustrated in the X-Ray’s investment growth graph. There,

the portfolio and benchmark returns are calculated by asset-weighting the monthly returns. The weights

are based on the investor’s inputs of initial investments. Consequently, the portfolio and benchmark

returns reflect the pretax results an investor would have achieved by rebalancing the portfolio on a

monthly basis.

It is important to note that the portfolio and benchmark returns are not based on the investment returns

that are shown in the X-Ray’s trailing return section (located above the portfolio returns). This is a

common mistake to make when looking at the investments’ trailing returns and the portfolio’s trailing

returns. The portfolio’s weighted returns are based on the investment growth graph, which assumes

monthly rebalancing. If one looks at investments’ trailing returns at different trailing time periods,

calculates a weighted average of these trailing returns at each trailing time period, compares the results

with the portfolio returns at different trailing time periods, one is comparing a monthly rebalanced series

(the portfolio’s series) with a series which that has been rebalanced at YTD, 1 month, 3 months and 1

year. These different values should not be compared.

For more information on how the X-Ray calculates portfolio return, please refer to the next section on the

investment growth graph.



38

Investment Growth Graph

An investment growth graph is available in the X-Ray’s PDF report. It shows the growth in value of 1000

currency units from an early investment date, as represented in Figure 2.c.

Figure 2.c (PDF Only)

The graph takes as its starting point the current weights of the portfolio holdings. Using these weights,

the X-Ray calculates the monthly weighted return going backwards in time. Then, from the earliest

possible date, the X-Ray assumes the investor invests 10,000 currency units. The invested amount is

then compounded forward using the monthly weighted returns.

A simple example might help to understand how the investment growth graph is generated. Assume two

funds, where the current investment weights are 25% and 75%.

Date Fund A Fund B Portfolio Return Values

April-10 5% 10% 8,75% € 1 216

Mar-10 3% 5% 4,5% € 1 118

Feb-10 4% 8% 7,0% € 1 070

Jan-10 € 1 000

If two funds within a portfolio have different inception dates, for example assume Fund A has history of

10 years and Fund B has a history of 5 years, the fund weighting within the portfolio is scaled when the

younger fund is added. Figure 2.d provides an example of this scaling within a portfolio of three funds

with different inception dates.



39

Figure 2.d

Note that the investment growth graph does not show the investor’s systematic investments or

divestments. It only shows the growth of 10,000 currency units from the earliest investment date of all

holdings to the latest month-end in Morningstar’s databases.

The current weights are estimated as follows:

At time t, the value of the investor’s investment in fund i is:

itiit navshcv *=

where:



The total value of the investor’s combined holdings is:

∑=

n

i

ithcv1

where:


Consequently, the investor’s current weight in holding i at time t is:



40

∑=

=n

i

it

it

it

hcv

hcvw

1



41

Risk / Reward Scatter Plot

The Risk / Reward Scatter Plot is based on each holding’s risk and return over the most recent three-year

period as Figure 2.e represents. Risk is measured as a three-year standard deviation of return. Return is

measured as a three year arithmetic mean return. The Risk / Reward Scatter Plot also contains the

portfolio’s risk and return, as well as the indicated benchmark’s risk and return.

Figure 2.e (PDF Only)

All figures and explanations to their algorithms can be found in this document’s performance section.

First, note that the X-Ray does not divide the risk figure with the reward figure, it is not an inverted

Sharpe measure. Instead, the X-Ray uses the figures as coordinates, where the risk figure is plotted on

the x-axis and the reward figure is plotted on the y-axis. From an analytical perspective, each increase on

the x-axis is an increase in risk. Given two funds with identical risk, a risk averse investor will prefer the

fund with the highest reward. In the Risk / Reward Scatter Plot, these two funds will be placed identically

vertically, but differently horizontally.

The mean calculation is determined in the traditional sense of an average, arithmetically. That is, the

mean will be calculated as the sum of a series of numbers divided by the count of that series of

numbers.



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If one assumes that investors get rewarded for taking risk, an investor who X-Rays a portfolio of 1,000

funds, each fund with slightly higher risk than the previous, the X-Ray’s Risk / Reward Scatter Plot

should, in theory, portray the thousand funds as a string of dots moving upwards from the southwest to

northeast.

Correlation Matrix

The performance correlation coefficients shown in the matrix are calculated using trailing monthly returns

converted into the currency of the portfolio over the most recent 3 Year time period, an example can be

seen in Figure 2.f.

Figure 2.f (PDF Only)

The calculation is performed using simple regressionwith intervals of correlation values color-coded for

clear graphical representation. Positive and negative coefficients are displayed using different colors.



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Appendix A: Sample X-Ray PDF Report

To help illustrate the definitions provided in this document, reference to an example X-Ray PDF are

available in Appendix A below.



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