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Pro Forma Development (Part II) Roger Staiger, FRICS Stage Capital, LLC (202) 640-8912 [email protected]

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Page 1: Pro Forma Development (Part II) - Amazon S3...Pro Forma Development (Part II) Roger Staiger, FRICS Stage Capital, LLC (202) 640-8912 rstaiger@stagecapitalllc.com Disclaimer All slides

Pro Forma Development

(Part II) Roger Staiger, FRICS

Stage Capital, LLC (202) 640-8912

[email protected]

Page 2: Pro Forma Development (Part II) - Amazon S3...Pro Forma Development (Part II) Roger Staiger, FRICS Stage Capital, LLC (202) 640-8912 rstaiger@stagecapitalllc.com Disclaimer All slides

Disclaimer All slides in this presentation are the intellectual property of Stage Capital, LLC and Roger Staiger, FRICS. Use of these slides is only permitted when presented by Roger Staiger, FRICS or a designee of Stage Capital, LLC. Further distribution is strictly prohibited.

Roger Staiger, FRICS [email protected] 2 of 53

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Structure 4-Part Sessions: 2-hours each Pro Forma Review Amortization: Custom Amortization

Rent Roll Draw Page Inflow/Outflow Risk Quantification

Roger Staiger, FRICS [email protected]

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Pro Forma Model 4-unit apartment building Adjusted to 39-unit (n-unit)

Based on Harvard Business Case Study: Revere Street (on Steroids)

MS Excel 2007/2010 Focused on Intermediate Modeling skills Result: completed scalable/modular pro forma

model

Roger Staiger, FRICS [email protected]

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Structure/Logic Flow (Part I)

Roger Staiger, FRICS [email protected]

Summary Page Pro Forma Page (s2)

Amortization Page (s3) Inputs Section

(s1)

Analysis (s4)

Page 6: Pro Forma Development (Part II) - Amazon S3...Pro Forma Development (Part II) Roger Staiger, FRICS Stage Capital, LLC (202) 640-8912 rstaiger@stagecapitalllc.com Disclaimer All slides

Structure/Logic Flow (Part II)

Roger Staiger, FRICS [email protected] 6 of 53

Summary Page

Pro Forma Page

Amortization Page (s1) Inputs Section

Analysis (Project)

Rent Roll Page (s2)

Construction Draw Page (s3)

Risk Quantification (Best/ML/Worst) (s4)

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Inputs Page (Pro Forma)

Roger Staiger, FRICS [email protected]

Equity

Debt

Uses

Revenue

Expenses

Finance

Valuation/ Sale

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Pro Forma

Roger Staiger, FRICS [email protected]

Uses

Debt

Equity = CF0

Rev

enue

Exp

Fnan

Rev

enue

Exp

S Exp

Princ

T+1

NI

CFT

NI NI

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Summary Page

Roger Staiger, FRICS [email protected] 9 of 53

Source 4,924,686     Operations # Units Avg SF Unit $/mo Finance I/PEquity 984,937         Efficiency 12 837.50          1,256           Tranche 1

Investor 1 984,937         One Bed 12 975.00          1,550           Principal Principal_T1 3,939,749      Investor 2 One Bed + De 6 1,250.00       1,800           Loan‐to‐Value LtV_T1 80%

Debt 3,939,749      Two Bed 9 1,450.00       2,300           Term (Years) Term_T1 20Tranche 1 3,939,749      39 Interest Rate Interest_T1 8.00%Tranche 2 ‐                 Vacancy 1 5.00% Structure (1:CPM, 2:I/O, 3:Custom) 2

Vacancy 2 5.00% Origination Fee Orig_Fee_T1 1.00%Uses 4,924,686     Vacancy 3 5.00% Tranche 2

Land & Related 1,000,000      Vacancy 4 5.00% Principal Principal_T2 ‐                  General & Administ 170,000         Term (Years) Term_T2 20Dev Chrgs & Mun C 110,000         Rental Escl 2.00% Interest Rate Interest_T2 15.00%Hard Cost Construc 3,401,500      Structure (1:CPM, 2:I/O, 3:Custom) 2Buidling Operation 60,000           Management per Net Rev 5.00% Origination Fee Orig_Fee_T2 1.00%Financing Expense 183,186         Repairs per Net Rev 5.00%

Janitor per Year 20,600         Valuation I/PHeat per Year 21,000         Capitalization Rate Cap_Rate 8.00%Electricity per Year 10,000         Sales Expense Sales_Exp 6.00%

Surplus/(Deficit) ‐                 Water per Year 12,000         Discount Rate Discount_Rate 10.00%Property Tax per Year 78,000        

PV Ops 1,213,645     46.37% Insurance per Year 32,000         Purchase/Dev Start Dev_Start 1‐Jan‐13PV Rev 1,403,507     53.63% Comm Operating Date COD 1‐Jan‐14

2,617,152     Expense Escl 2.00% Sales Period Sale_Term_Yr 10                   CF0 (1,059,622)  NPV 1,557,530     DSCR Minimum 0.56            Case (Best ‐ 1; ML ‐ 2; Worst ‐ 3) 2                      IRR 27.03% Cash‐on‐Cash (monthly) Minimum 1.50%

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Summary Page (Bottom)

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Valuation:Year 1 2 3 4 5 6 7 8 9 10

RevenueRental 782,100      797,742         813,697    829,971        846,570      863,502   880,772         898,387        916,355           934,682         Vacancy 39,105         39,887           40,685       41,499          42,329         43,175     44,039           44,919          45,818             46,734            

Total Revenue 742,995      757,855        773,012    788,472       804,242      820,327  836,733        853,468       870,537          887,948         

ExpenseManagement 37,150         37,893           38,651       39,424          40,212         41,016     41,837           42,673          43,527             44,397            Repairs 37,150         37,893           38,651       39,424          40,212         41,016     41,837           42,673          43,527             44,397            Janitor 20,790         21,210           21,638       22,074          22,520         22,974     23,438           23,911          24,394             24,886            Heat 21,194         21,621           22,058       22,503          22,957         23,421     23,893           24,376          24,868             25,370            Electricity 10,092         10,296           10,504       10,716          10,932         11,153     11,378           11,607          11,842             12,081            Water 12,111         12,355           12,604       12,859          13,118         13,383     13,653           13,929          14,210             14,497            Property Tax 78,719         80,308           81,929       83,583          85,270         86,991     88,747           90,538          92,365             94,230            Insurance 32,295         32,947           33,612       34,290          34,982         35,688     36,409           37,144          37,893             38,658            

Total Expenses 249,500      254,522        259,645    264,872       270,204      275,643  281,191        286,851       292,626          298,516         

Net Operating Income 493,495      503,333        513,367    523,600       534,038      544,684  555,542        566,616       577,911          589,432         

DebtTranche 1 315,180      315,180         315,180    315,180        315,180      315,180   315,180         315,180        315,180           315,180         Tranche 2 ‐               ‐                 ‐             ‐                 ‐               ‐           ‐                 ‐                ‐                    ‐                  

Total Debt 315,180      315,180        315,180    315,180       315,180      315,180  315,180        315,180       315,180          315,180         

Net Sales Proceeds ‐              ‐                 ‐            ‐                ‐              ‐           ‐                 ‐                ‐                   3,124,136     

Reversion FCF ‐              ‐                 ‐            ‐                ‐              ‐           ‐                 ‐                ‐                   3,124,136     Operating FCF 178,315      188,153        198,187    208,420       218,858      229,504  240,362        251,436       262,731          274,252         

Total FCF (984,937)       178,315      188,153        198,187    208,420       218,858      229,504  240,362        251,436       262,731          3,398,388     

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Amortization Page

Roger Staiger, FRICS [email protected]

Tranche 1 Tranche 2Principal 3,939,749  Principal ‐          Interest 8.00% Interest 15.00%Term 20 Term 20I/O 2 I/O 2

100.00% 100.00%# BoP Principal Interest Payment EoP Custom # BoP Principal Interest Payment EoP Custom1 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 1 ‐           ‐           ‐           ‐           ‐           0.42%2 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 2 ‐           ‐           ‐           ‐           ‐           0.42%3 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 3 ‐           ‐           ‐           ‐           ‐           0.42%4 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 4 ‐           ‐           ‐           ‐           ‐           0.42%5 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 5 ‐           ‐           ‐           ‐           ‐           0.42%6 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 6 ‐           ‐           ‐           ‐           ‐           0.42%7 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 7 ‐           ‐           ‐           ‐           ‐           0.42%8 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 8 ‐           ‐           ‐           ‐           ‐           0.42%9 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 9 ‐           ‐           ‐           ‐           ‐           0.42%10 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 10 ‐           ‐           ‐           ‐           ‐           0.42%11 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 11 ‐           ‐           ‐           ‐           ‐           0.42%12 3,939,749  ‐               26,265        26,265     3,939,749  0.42% 12 ‐           ‐           ‐           ‐           ‐           0.42%

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Pro Forma Page Completed (Top Section)

Roger Staiger, FRICS [email protected] 12 of 53

Periods 1 2 3 4 5 6 7 8 9 10 11 12Month Jan‐14 Feb‐14 Mar‐14 Apr‐14 May‐14 Jun‐14 Jul‐14 Aug‐14 Sep‐14 Oct‐14 Nov‐14 Dec‐14

Revenue Year 1 1 1 1 1 1 1 1 1 1 1 1Efficiency 15,075        15,075     15,075     15,075     15,075     15,075     15,075     15,075     15,075     15,075     15,075     15,075    One Bed 18,600        18,600     18,600     18,600     18,600     18,600     18,600     18,600     18,600     18,600     18,600     18,600    One Bed + Den 10,800        10,800     10,800     10,800     10,800     10,800     10,800     10,800     10,800     10,800     10,800     10,800    Two Bed 20,700        20,700     20,700     20,700     20,700     20,700     20,700     20,700     20,700     20,700     20,700     20,700    

Total Rent 65,175       65,175    65,175    65,175    65,175    65,175    65,175    65,175    65,175    65,175    65,175    65,175   

Vacancy 1 754             754           754           754           754           754           754           754           754           754           754           754          Vacancy 2 930             930           930           930           930           930           930           930           930           930           930           930          Vacancy 3 540             540           540           540           540           540           540           540           540           540           540           540          Vacancy 4 1,035          1,035       1,035       1,035       1,035       1,035       1,035       1,035       1,035       1,035       1,035       1,035      

Total Vacancy 3,259         3,259       3,259       3,259       3,259       3,259       3,259       3,259       3,259       3,259       3,259       3,259      

Total Revenue 61,916       61,916    61,916    61,916    61,916    61,916    61,916    61,916    61,916    61,916    61,916    61,916   

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Analysis/Valuation (Bottom of Pro Forma)

Roger Staiger, FRICS [email protected]

Valuation: Dec‐13 Jan‐14 Feb‐14 Mar‐14 Apr‐14 May‐14 Jun‐14 Jul‐14 Aug‐14 Sep‐14 Oct‐14Total FCF (1,059,622)  14,993       14,969    14,945    14,921    14,896    14,872    14,848    14,823    14,799    14,775   

DSCR 0.57            0.57         0.57         0.57         0.57         0.57         0.57         0.56         0.56         0.56        Minimum 0.56           

Cash‐on‐Cash 1.52% 1.52% 1.52% 1.51% 1.51% 1.51% 1.51% 1.51% 1.50% 1.50%Minimum 1.50%

PV Reversion 1,213,645    46.37%PV Operating 1,403,507    53.63%

2,617,152   CF0 (1,059,622) Net Present Value 1,557,530   IRR 27.03%

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Unit Characteristics

Roger Staiger, FRICS [email protected] 14 of 53

Periods 1 2 3 4 5 6Months Jan‐14 Feb‐14 Mar‐14 Apr‐14 May‐14 Jun‐14

Unit # Unit Type Area SF Rental Rate ($/mo) Year 1 1 1 1 1 11 Efficiency 800 1200 1 1,200           1,200       1,200       1,200       1,200       1,200      2 Efficiency 825 1250 2 1,250           1,250       1,250       1,250       1,250       1,250      3 Efficiency 850 1275 3 1,275           1,275       1,275       1,275       1,275       1,275      4 Efficiency 875 1300 4 1,300           1,300       1,300       1,300       1,300       1,300      5 Efficiency 800 1200 5 1,200           1,200       1,200       1,200       1,200       1,200      6 Efficiency 825 1250 6 1,250           1,250       1,250       1,250       1,250       1,250      7 Efficiency 850 1275 7 1,275           1,275       1,275       1,275       1,275       1,275      8 Efficiency 875 1300 8 1,300           1,300       1,300       1,300       1,300       1,300      9 Efficiency 800 1200 9 1,200           1,200       1,200       1,200       1,200       1,200      10 Efficiency 825 1250 10 1,250           1,250       1,250       1,250       1,250       1,250      11 Efficiency 850 1275 11 1,275           1,275       1,275       1,275       1,275       1,275      12 Efficiency 875 1300 12 1,300           1,300       1,300       1,300       1,300       1,300      13 One Bed 950 1500 13 1,500           1,500       1,500       1,500       1,500       1,500      14 One Bed 975 1550 14 1,550           1,550       1,550       1,550       1,550       1,550      

Summary Table12 Efficiency 837.50      1,256.25                        Efficiency 15,075         15,075     15,075     15,075     15,075     15,075    12 One Bed 975.00      1,550.00                        One Bed 18,600         18,600     18,600     18,600     18,600     18,600    6 One Bed + Den 1,250.00   1,800.00                        One Bed + Den 10,800         10,800     10,800     10,800     10,800     10,800    9 Two Bed 1,450.00   2,300.00                        Two Bed 20,700         20,700     20,700     20,700     20,700     20,700    39

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Development (Today)

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Development Start 1‐Jan‐13Construction Months 12Opening Date 1‐Jan‐14

1 2 3 4 5 6 7Cost Item Jan‐13 Feb‐13 Mar‐13 Apr‐13 May‐13 Jun‐13 Jul‐13

Land & Related Land_Rela 1,000,000 Land & Related 1,000,000 100.00%

General & Administrative G_A 170,000 Legal Fees 20,000 8.33% 8.33% 8.33% 8.33% 8.33% 8.33% 8.33%Development Management Fees 60,000 8.33% 8.33% 8.33% 8.33% 8.33% 8.33% 8.33%Insurance & Warranty 60,000 8.33% 8.33% 8.33% 8.33% 8.33% 8.33% 8.33%Other G&A 30,000 8.33% 8.33% 8.33% 8.33% 8.33% 8.33% 8.33%

Dev Chrgs & Mun Costs Dev_Chrg_ 110,000 Development Charges 85,000 8.33% 8.33% 8.33% 8.33% 8.33% 8.33% 8.33%Building Permits 20,000 8.33% 8.33% 8.33% 8.33% 8.33% 8.33% 8.33%Municipal Costs 5,000 8.33% 8.33% 8.33% 8.33% 8.33% 8.33% 8.33%

Hard Cost Construction HC_Const 3,401,500 General Costs 1,500,000 0.62% 1.65% 4.41% 9.18% 14.99% 19.15% 19.15%Site Work 450,000 0.62% 1.65% 4.41% 9.18% 14.99% 19.15% 19.15%

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Development (cont’d) (Today)

Roger Staiger, FRICS [email protected] 16 of 53

Cost Item

Land & Related 1,000,000            ‐                  ‐                  ‐                  ‐                  ‐                ‐               Land & Related 1,000,000             ‐                  ‐                  ‐                  ‐                  ‐                ‐               

General & Administrative 14,167                 14,167           14,167           14,167           14,167           14,167         14,167        Legal Fees 1,667                    1,667              1,667              1,667              1,667              1,667            1,667           Development Management Fees 5,000                    5,000              5,000              5,000              5,000              5,000            5,000           Insurance & Warranty 5,000                    5,000              5,000              5,000              5,000              5,000            5,000           Other G&A 2,500                    2,500              2,500              2,500              2,500              2,500            2,500           

Dev Chrgs & Mun Costs 9,167                    9,167              9,167              9,167              9,167              9,167           9,167          Development Charges 7,083                    7,083              7,083              7,083              7,083              7,083            7,083           Building Permits 1,667                    1,667              1,667              1,667              1,667              1,667            1,667           Municipal Costs 417                        417                  417                  417                  417                  417               417              

Hard Cost Construction 21,122                 56,262           149,860         312,421         509,825         651,260       651,260      General Costs 9,314                    24,811            66,086            137,772          224,823          287,194        287,194       Site Work 2,794                    7,443              19,826            41,332            67,447            86,158          86,158         

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Development (cont’d) (Today)

Roger Staiger, FRICS [email protected] 17 of 53

Development Cash Flow:Equity BoP 984,937                ‐                  ‐                  ‐                  ‐                  ‐                ‐               Equity Draw 984,937                ‐                  ‐                  ‐                  ‐                  ‐                ‐               Equity EoP ‐                        ‐                  ‐                  ‐                  ‐                  ‐                ‐               Equity FV * Financial Close Equity_COD 1,059,622           1,059,622             ‐                  ‐                  ‐                  ‐                  ‐                ‐               

Construction Debt BoP ‐                        99,288            180,538          357,579          701,228          1,248,054    1,942,455   Construction Debt Interest 143,789               ‐                        662                  1,204              2,384              4,675              8,320            12,950         Construction Debt Draw 99,288                  80,588            175,837          341,265          542,151          686,081        686,081       Construction Debt EoP 99,288                  180,538          357,579          701,228          1,248,054       1,942,455    2,641,485   

Z‐Score (2.50)                     (2.00)               (1.50)               (1.00)               (0.50)               ‐                0.50             

S‐Curve 0.62% 2.28% 6.68% 15.87% 30.85% 50.00% 69.15%Draw 100.00% 0.62% 1.65% 4.41% 9.18% 14.99% 19.15% 19.15%

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Risk

Scenario Analysis

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19 of 53

Risk Variability of returns from an investment Quantified as variance and standard

deviation about an expected outcome (sample mean)

Types 1. Systematic (Market – not diversifiable) 2. Unsystematic (Unique/Security Specific –

diversifiable)

Roger Staiger, FRICS [email protected]

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20 of 53

Risk - Variability

X-bar

Spread/Dispersion (σ)

Roger Staiger, FRICS [email protected]

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21 of 53

Return Equity investor’s share of company’s

earnings Forms

1. Earnings Distributed 2. Earnings Reinvested

Expected value to be earned on initial investment

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Equity Return – Methods to Calculate

factorsmicmacroeconoreturn to Relates -

)(...)()()()((APT)Theory Pricing Arbitrage 3.

)]()([)()((CAPM) Model PricingAsset Capital 2.

)(...)()()(Return of Rate Expected 1.

2211 nnfi

ifMfi

ZBA

rbrbrbRERE

RERERERE

KZPKBPKAPRE

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Risk and Return Markowitz is father of modern portfolio theory Relates to fully diversified ‘efficient’ portfolio Goal: Maximize Return for each Risk level

E(R)

(Risk)

Efficient Frontier (Efficient Portfolios)

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Measures of Central Locations (Return)

1. Mean Measure of central location Affected by outliers

2. Median Central value in data set when numbers are arranged in

ascending or descending order

3. Mode Data value which occurs with greatest frequency

4. Interquartile Range (IQR) Data separation into quarters (LIBOR calculation)

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Measures of Dispersion (Risk)

1. Range • Distance from largest to smallest value

2. Variance (sample) • Measure of dispersion utilizing all data values • Deviations about mean are squared

LowHi ValValRange

1

2

2

n

xxS i

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Standard Deviation (scenario) Symbol () Positive Square Root of Variance Measured in base units Same units as mean

ii PrErES2

)()()(

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Standard Deviation (sample) Symbol () Positive Square Root of Variance Measured in base units Same units as mean

1

1)(

2

n

xxS i

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Population versus Sample

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1

1 vs

11

2

1

2

n

xx

N

xt

ii

s

t

ii

p

Roger Staiger, FRICS [email protected]

11:;1:

n

PN

P isip

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Skewness Measure of symmetry for a distribution Exists when Mean Median Mode Third moment about mean

3

1

3/

S

nxxSkewness

n

ii

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Skewness (cont’d) Standard Normal Curve Skewness = 0

Positive (Rightward Skew) Mean > Median > Mode Rightward Tail

Negative (Leftward Skew) Mean < Median < Mode

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Skewness (cont’d) Positive

Negative (Tail Risk)

Mode Median

Mean

Mode Median

Mean

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Kurtosis Measure of Peakedness Fourth moment about the mean

4

1

4/

S

nxxKurtosis

n

ii

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Kurtosis (cont’d) Standard Normal Curve Kurtosis = 3.0 (some correct and make 0.0)

Platykurtic (Flat) Kurtosis < 3.0

Leptokurtic (Peaked) Kurtosis > 3.0

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Kurtosis (cont’d)

X-bar

Standard Normal (Kurtosis = 3.0)

Leptokurtic (Kurtosis > 3.0)

Platykurtic (Kurtosis < 3.0)

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Measures of Efficiency Efficiency – The ratio of Risk and Reward Goal: Maximize reward for any risk level - Markowitz Portfolio Theorty Measures 1. Coefficient of Variation (CV) (Goal: Minimize)

2. Sharpe Ratio (Goal: Maximize)

3. Treynor Ratio (Goal: Maximize)

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Coefficient of Variation (CV) Descriptive statistic relating standard deviation to

mean; measure of efficiency (unitless) Required to quantify Return OF Capital Useful when comparing data sets with different

means and standard deviations

Measures relative size of standard deviation to mean

Goal: Minimize Roger Staiger, FRICS [email protected]

xCV

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Sharpe Ratio Similar to Coefficient of Variation Reciprocal adjusted for purchasing power Industry standard measure of efficiency Reward to Risk Ratio (Goal: Maximize)

37 of 53

fRX

SR

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Treynor Ratio Similar to Sharpe Ratio Normalized to portfolio beta Reward to Risk Ratio (Goal: Maximize) Requires calculation of portfolio beta

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p

fRXTR

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Measures of Linear Association between Two Variables (1)

Covariance Descriptive measure of the linear

association between two variables

iprelationshlinear better Sxy larger statenot Can es.in variabl expressed unitson depends Value *

iprelationshlinear no indicatesSxy Zero(3)iprelationshlinear negative indicatesSxy Negative (2)

iprelationshlinear positive indicatesSxy Positive (1)*:Note

1

n

YYXXS ii

xy

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Measures of Linear Association (2)

iprelationshlinear no indicates 0 -iprelationshlinear negativeperfect indicates 1- -iprelationshlinear positiveperfect indicates 1 -

1- to1 Range -

tCoefficienn Correlatio

yx

xyxy SS

Sr

Covariance Sample Means

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Measures of Linear Association (3) Coefficient of Determination Measure of Goodness of Fit Range 0 – 1 (zero to one) Used in regression analysis as determinant

of strength NOT a Test Statistics Must be used after T- and F- Statistics determine

statistically significant relationship

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SSTSSRr 2

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Probability Distribution A listing of all possible outcomes, or

events, with a probability (chance of occurrence) assigned to each outcome

Types: 1. Discrete

2. Continuous

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Probability Distribution (Internal Rate of Return (IRR))

Continuous Distribution Statistical Certainty 100% not accurate

Decisions based on IRR value?! Valid???

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Expected Rate of Return E(r) Rate of return expected to be realized from

an investment Weighted average of the probability

distribution of possible results

ievent ofy Probabilit ievent h Return wit Expected )(

:where

)()(1

i

i

n

iii

PRE

PRERE

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Scenario Risk Weighted average outcome standard

deviations proportioned with probability of occurrence Provides idea of how far above or below

expected value actual value may be

n

iii PrErE

1

2

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Probability

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Coefficient of Variation Normalize risk to Expected return

P

n

iii

P RE

PrErE

REcv

1

2

* Used to Compare return risk of different portfolios

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Coefficient of Variation (CV) Addresses first (and most important)

investment goal: 1) Return OF Capital Primary

2) Return ON Capital Secondary

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Z-Score

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xxZ i

Negative reciprocal of CV

At xi = 0; 100% of capital returns with 0.0% return

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Z-Score (cont’d)

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0 1 -1

68% of Data

P(Gain)

P(Loss)

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50 of 53

Normal Distribution Securities modeled using normal

distribution Mean = Median (no skewing) Most likely value (X-bar) Equally probably value above X-bar as

below Expected value more likely closer to X-bar

than farther

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51 of 53

Normal Distribution (cont’d)

X-bar

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Warning!

Roger Staiger, FRICS [email protected] 52 of 53

Will entertain all questions

May be slow for more advanced Excel users

At end will produce working, scalable pro forma

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Questions?

Let’s Begin (see memorandum for detailed steps of

process at conclusion)