Financial Analysts Awareness Program

Dr. Mounther Barakat Securities and Commodities Authority

1-1

نييلاملا نيللحملا جمانرب يرمعلا تاكرب رذنم .

د علسلاو ةيلاملا قارولاا ةئيه

1-2

Forecasting Example Balance sheet, in millions of dollars Cash & sec.

Accounts rec.

Inventories Total CA Net fixed assets Total assets $ 20 Accts. pay. & accruals 240 Notes payable 240 Total CL $ 500 L-T debt Common stock Retained 500 earnings $1,000 Total claims $ 100 100 $ 200 100 500 200 $1,000

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Forecasting Example

Income statement, in millions of dollars Sales Less: Var. costs (60%) Fixed costs EBIT Interest EBT Taxes (40%) Net income Dividends (30%) Add’n to RE $2,000.00

1,200.00

700.00

$ 100.00

16.00

$ 84.00

33.60

$ 50.40

$15.12

$35.28

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Key assumptions

     Operating at full capacity in 2006.

Each type of asset grows proportionally with sales.

Payables and accruals grow proportionally with sales.

2006 profit margin (2.52%) and payout (30%) will be maintained.

Sales are expected to increase by $500 million. (%GS = 25%)

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Determining additional funds needed AFN AFN = (A*/S 0 )ΔS – (L*/S 0 ) ΔS – M(S 1 )(RR) = ($1,000/$2,000)($500) – ($100/$2,000)($500) – 0.0252($2,500)(0.7) = $180.9 million.

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How shall AFN be raised?

 The payout ratio will remain at 30 percent (d = 30%; RR = 70%).

 No new common stock will be issued.

 Any external funds needed will be raised as debt, 50% notes payable and 50% L-T debt.

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Sales Less: VC FC EBIT Interest EBT Taxes (40%) Net income Forecasted Income Statement 2006 $2,000 1,200 700 $ 100 16 $ 84 34 $ 50 Forecast Basis 1.25

0.60

0.35

2007 Forecast $2,500 1,500 875 $ 125 16 $ 109 44 $ 65 Div. (30%) Add’n to RE $15 $35 $19 $46

1-8

Forecasted Balance Sheet (2007) - Assets Cash Accts. rec.

Inventories Total CA Net FA Total assets 2006 $ 20 240 240 $ 500 500 $1,000 Forecast Basis 0.01

0.12

0.12

0.25

2007 1 st Pass $ 25 300 300 $ 625 625 $1,250

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Forecasted Balance Sheet (2007) - Liabilities and Equity AP/accruals Notes payable Total CL L-T debt Common stk.

Ret.earnings

Total claims 2006 $ 100 100 $ 200 100 500 200 $1,000 Forecast Basis 0.05

+46* 2007 1 st Pass $ 125 100 $ 225 100 500 246 $1,071

* From income statement.

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What is the additional financing needed (AFN)?

 Required increase in assets  Spontaneous increase in liab.

 Increase in retained earnings  Total AFN = $ 250 = $ 25 = $ 46 = $ 179 The company must have the assets to generate forecasted sales. The balance sheet must balance, so we must raise $179 million externally.

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How will the AFN be financed?

  Additional N/P  0.5 ($179) = $89.50

Additional L-T debt  0.5 ($179) = $89.50

 But this financing will add to interest expense, which will lower NI and retained earnings. This will lower equity financing and increase debt financing, and so on. We will generally ignore financing feedbacks.

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Forecasted Balance Sheet (2007) - Assets Cash Accts. rec.

Inventories Total CA Net FA Total assets 2007 1 st Pass $ 25 300 300 $ 625 625 $1,250 AFN 2007 2 nd Pass $ 25 300 300 $ 625 625 $1,250

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Forecasted Balance Sheet (2007) - Liabilities and Equity AP/accruals Notes payable Total CL L-T debt Common stk.

Ret.earnings

Total claims 2007 1 st Pass $ 125 100 $ 225 100 500 246 $1,071 AFN +89.5

+89.5

2007 2 nd Pass $ 125 190 $ 315 189 500 246 $1,250

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Advanced Forecasting

 Use of regressions for each item  Use of iterations in finding interest income and expense  Forecasting with stock dividends, stock repurchase, stock issuance, stock splits, ….

1-15

Analyzing PE and PB and its Usages Case I

0% 100% 10% =ومنلا =عيزوتلا =بولطملا دئاعلا :لاح يف ريعستلا ومن دوجو مدع ةيدقن تاعرزوت لكش ىلع حابرلأا ةفاك عفدت )اهدوجو مدع وأ ةفاضم ةيداصتقا ةميق دوجو( همدع وأ ةيدايتعا ريغ حابرا دوجو هنم ربكأ وأ بولطملا دئاعلا يواسي ققحتملا دئاعلا نا يأ قوس يأ وأ راكتحا وأ ةسفانم قوس بولطملا دئاعلا لدعم/مهسلا ةيحبر = رعسلا

1-16

Analyzing PE and PB and its Usages Case I

راكتحأ ةسفانم 10 10% 3 1 2 30% 3 10 10% 2 1 1 20% 2 10 10% 1 1 0 10% 1 ةيرتفدلا ةميقلا بولطملا دئاعلا يلكلا حبرلا يداعلا حبرلا يداع ريغلا حبرلا ققحتملا دئاعلا عيزوتلا ةيرتفدلا ةميقلا 10 10 10 30 3 20 2 10 1 يقوسلا رعسلا ةيرتفدلا ةميقلا فعاضم ةيرتفدلا ةميقلا ىلا ةيقوسلا ةميقلا 10 10 10 )ةيحبرلا فعاضم( ةيحبرلا ىلا ةيقوسلا ةميقلا لا مأ ةفاضم ةميق دوجو نع رظنلا ضغب اتباث ةيحبرلا فعاضم ىقبيو ةيرتفدلا ةميقلا فعاضم ريغتي

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Analyzing PE and PB and its Usages Case II

0.05

0.5

0.1

0.1

=ومنلا =عيزوتلا =بولطملا دئاعلا =ققحتملا دئاعلا :لاح يف ريعستلا ومن دوجو رخلآا اهفصن زجحيو ةيدقن تاعيزوت لكش ىلع حابرلأا فصن عفدي ومنلا ليومتل )ةفاضم ةيداصتقا ةميق دوجو مدع( ةيدايتعا ريغ حابرا دوجو مدع عقوتم وه امم رثكأ سيلو طقف بولطملا دئاعلا يواسي ققحتملا دئاعلا نا يأ ةكرشلا مجح ةدايزل رامثتساو ةسفانم قوس )ومنلا لدعم-بولطملا دئاعلا لدعم(/)ومنلا لدعم+1(*تاعيزوتلا = رعسلا

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Analyzing PE and PB and its Usages Case II

5 12.16

10% 1.216

1.216

0 10% 0.608

12.76

12.76

1 10.5

4 3 2 1 ةنسلا 11.58

10% 1.158

1.158

11.03

10% 1.103

1.103

10.5

10% 1.05

1.05

10 10% 1 1 ةيرتفدلا ةميقلا بولطملا دئاعلا يلكلا حبرلا يداعلا حبرلا 0 10% 0.579

12.16

12.16

1 0 10% 0.551

11.58

11.58

1 0 10% 0.525

11.03

11.03

1 0 10% 0.5

10.5

10.5

1 يداع ريغلا حبرلا ققحتملا دئاعلا عيزوتلا ةيرتفدلا ةميقلا يقوسلا رعسلا ةيرتفدلا ةميقلا فعاضم ةيرتفدلا ةميقلا ىلا ةيقوسلا ةميقلا 10.5

10.5

10.5

10.5

)ةيحبرلا فعاضم( ةيحبرلا ىلا ةيقوسلا ةميقلا اتباث رمتسا هنكلو ومنلا ببسب ةيحبرلا فعاضم داز عقوتملا نم ربكأ ومن دجوي لا هنلأ اتباث يقب ةيرتفدلا ةميقلا فعاضم نأ لاإ ةكرشلا يف ومنلا نم مغرلاب عقوتملا نم ربكأ ومن دجوي لا هنلأ اتباث يقب ةيحبرلا فعاضم نأ لاإ ةكرشلا يف ومنلا نم مغرلاب

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Analyzing PE and PB and its Usages Case III

0.05

0.5

0.1

0.2

=ومنلا =عيزوتلا =بولطملا دئاعلا =ققحتملا دئاعلا :لاح يف ريعستلا ومن دوجو رخلآا اهفصن زجحيو ةيدقن تاعيزوت لكش ىلع حابرلأا فصن عفدي ومنلا ليومتل )ةفاضم ةيداصتقا ةميق دوجو( ةيدايتعا ريغ حابرا دوجو بولطملا دئاعلا نم ربكأ ققحتملا دئاعلا نا يأ ةكرشلا مجح ةدايزل رامثتساو ةسفانم قوس )ومنلا لدعم-بولطملا دئاعلا لدعم(/ةيدايتعلاا ريغ حابرلأا + ةيرتفدلا ةميقلا = رعسلا

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Analyzing PE and PB and its Usages Case III

5 14.64

10% 2.928

1.464

1.464

20% 1.464

1.464

16.11

45.39

2.818

15.5

4 13.31

10% 2.662

1.331

1.331

20% 1.331

1.331

14.64

41.26

2.818

15.5

3 12.1

10% 2.42

1.21

1.21

20% 1.21

1.21

13.31

37.51

2.818

15.5

2 11 10% 2.2

1.1

1.1

20% 1.1

1.1

12.1

34.1

2.818

15.5

1 10 10% 2 1 1 20% 1 1 11 31 2.818

15.5

ةنسلا ةيرتفدلا ةميقلا بولطملا دئاعلا يلكلا حبرلا يداعلا حبرلا يداع ريغلا حبرلا ققحتملا دئاعلا عيزوتلا ةزوجحملا حابرلأا ةيرتفدلا ةميقلا يقوسلا رعسلا ةيرتفدلا ةميقلا فعاضم ةيرتفدلا ةميقلا ىلا ةيقوسلا ةميقلا )ةيحبرلا فعاضم( ةيحبرلا ىلا ةيقوسلا ةميقلا اتباث رمتسا هنكلو ومنلا ببسب ةيحبرلا فعاضم داز اتباث ةيرتفدلا ةميقلا فعاضم ىقبي اتباث يقب ةيحبرلا فعاضم نأ لاإ ةكرشلا يف ومنلا نم مغرلاب

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Analyzing PE and PB and its Usages Case IV

0.05

0.05

0.5

=ومنلا =عيزوتلا 0.1

0.2

=بولطملا دئاعلا =ققحتملا دئاعلا = ةيدايتعلا ريغ حابرلأا ومن :لاح يف ريعستلا ومن دوجو رخلآا اهفصن زجحيو ةيدقن تاعيزوت لكش ىلع حابرلأا فصن عفدي ومنلا ليومتل )ةفاضم ةيداصتقا ةميق دوجو( ةيدايتعا ريغ حابرا دوجو بولطملا دئاعلا نم ربكأ ققحتملا دئاعلا نا يأ ةيدايتعلاا ريغ حابرلأا يف ومن ةكرشلا مجح ةدايزل رامثتساو ةسفانم قوس )ومنلا لدعم-بولطملا دئاعلا لدعم(/ةيدايتعلاا ريغ حابرلأا + ةيرتفدلا ةميقلا = رعسلا

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Analyzing PE and PB and its Usages Case IV

5 15.06

10% 3.66

1.506

2.262

24% 1.83

1.83

16.89

62.57

3.705

17.09

4 13.5

10% 3.124

1.35

1.864

23% 1.562

1.562

15.06

52.63

3.495

16.85

3 12.16

10% 2.68

1.216

1.538

22% 1.34

1.34

13.5

44.45

3.294

2 11 10% 2.31

1.1

1.271

21% 1.155

1.155

12.16

37.68

3.1

1 10 10% 2 1 1 20% 1 1 11 31 2.818

ةنسلا ةيرتفدلا ةميقلا بولطملا دئاعلا يلكلا حبرلا يداعلا حبرلا يداع ريغلا حبرلا ققحتملا دئاعلا عيزوتلا ةزوجحملا حابرلأا ةيرتفدلا ةميقلا يقوسلا رعسلا ةيرتفدلا ةميقلا فعاضم ةيرتفدلا ةميقلا ىلا ةيقوسلا ةميقلا )ةيحبرلا فعاضم( ةيحبرلا ىلا ةيقوسلا ةميقلا 16.59

16.31

15.5

ةيدايتعلاا ريغ حابرلأا يف ومنلا عم ةدرطم ةدايزبو ومنلا ببسب ةيحبرلا فعاضم داز ةيدايتعلاا ريغ حابرلأا يف ومنلا عم ةدرطم ةدايزبو ومنلا ببسب ةيرتفدلا ةميقلا فعاضم داز ةيدايتعلاا ريغ حابرلاا يف ومنلا عم نيفعاضملا دادزي

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Analyzing PE and PB and its Usages Conclusions

 Reinvestment of free cash flow at rates of return in excess of capital costs creates growth in abnormal earnings, resulting in valuation multiple expansion.

P

0

E

1   1 

r

The PE is a function of the prospective growth in future abnormal earnings.

1

E

1 *   (

r



rnings

( 1 

g

)

g

) 

r

    Usages of PE in any other cases will result in mispricing and arbitrage opportunities.

This huge limitation should be considered among many

other ones

.

1-24

Analyzing PE and PB and its Usages Conclusions

 Which PE to use the historical average of the same firm’s PE’s, OR  The PE of similar firms, OR  The PE of the industry  How are PE’s used for companies that have more than one division (weighted average?!)

1-25

Analyzing PE and PB and its Usages Conclusions

    PE does take risk into account indirectly (i.e. through the used pricing model’s discount rate).

PE gives the dollar amount (Price) the investor is willing to pay for one dollar of continued earnings. PE is the reciprocal of the required rate of return.

Empirical studies show that the required rate of return (calculated using other return models like the market model or CAPM) is usually different from the one calculated by PE ratios.

Only sustainable earnings are used, transitory or non recurring earnings

must

be excluded.

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Analyzing PE and PB and its Usages Recommendations

 Use PE ratios with maximum caution  Know when it is used and what it means  PB is also problematic some times, it is used when there are abnormal returns regardless whether they grow or not.

1-27

Cash A/R Inventories Total CA Gross FA Less: Dep.

Net FA Total Assets

Balance Sheet: Assets

2006 7,282 632,160 1,287,360 1,926,802 1,202,950 263,160 939,790 2,866,592 2005 57,600 351,200 715,200 1,124,000 491,000 146,200 344,800 1,468,800

1-28

Balance sheet: Liabilities and Equity Accts payable Notes payable Accruals Total CL Long-term debt Common stock Retained earnings Total Equity Total L & E 2006 524,160 636,808 489,600 1,650,568 723,432 460,000 32,592 492,592 2,866,592 2005 145,600 200,000 136,000 481,600 323,432 460,000 203,768 663,768 1,468,800

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Sales COGS Other expenses EBITDA Depr. & Amort.

EBIT Interest Exp.

EBT Taxes Net income

Income statement

2006 6,034,000 5,528,000 519,988 (13,988) 116,960 (130,948) 136,012 (266,960) (106,784) (160,176) 2005 3,432,000 2,864,000 358,672 209,328 18,900 190,428 43,828 146,600 58,640 87,960

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No. of shares EPS DPS Stock price

Other data

2006 100,000 DHS 1.602

DHS 0.11

DHS 2.25

2005 100,000 DHS 0.88

DHS 0.22

DHS 8.50

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Statement of Retained Earnings (2006) Balance of retained earnings, 12/31/05 Add: Net income, 2006 Less: Dividends paid Balance of retained earnings, 12/31/06 DHS 203,7 68 (160,176) (11,000) $32,592

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Statement of Cash Flows (2006)

OPERATING ACTIVITIES Net income Add (Sources of cash): Depreciation Increase in A/P Increase in accruals Subtract (Uses of cash): Increase in A/R Increase in inventories Net cash provided by ops.

(160,176) 116,960 378,560 353,600 (280,960) (572,160) (164,176)

1-33

Statement of Cash Flows (2006)

L-T INVESTING ACTIVITIES Investment in fixed assets FINANCING ACTIVITIES Increase in notes payable Increase in long-term debt Payment of cash dividend Net cash from financing NET CHANGE IN CASH Plus: Cash at beginning of year Cash at end of year (711,950) 436,808 400,000 (11,000) 825,808 (50,318) 57,600 7,282

1-34

Notes from the statement of CFs?

 Net cash from operations = -$164,176, mainly because of negative NI.

 The firm borrowed $825,808 to meet its cash requirements.

 Even after borrowing, the cash account fell by $50,318.

1-35

Did the expansion create additional net operating after taxes (NOPAT)?

NOPAT = EBIT (1 – Tax rate) NOPAT 06 = -$130,948(1 – 0.4) = -$130,948(0.6) = -$78,569 NOPAT 05 = $114,257

1-36

What effect did the expansion have on net operating working capital?

NOWC = Current Non-interest assets bearing CL NOWC 06 = ($7,282 + $632,160 + $1,287,360) – ( $524,160 + $489,600) = $913,042 NOWC 05 = $842,400

1-37

What effect did the expansion have on operating capital?

Operating capital = NOWC + Net Fixed Assets Operating Capital 06 = $913,042 + $939,790 = $1,852,832 Operating Capital 05 = $1,187,200

1-38

What is your assessment of the expansion’s effect on operations?

Sales NOPAT NOWC Operating capital Net Income 2006 $6,034,000 -$78,569 2005 $3,432,000 $114,257 $913,042 $1,852,832 -$160,176 $842,400 $1,187,200 $87,960

1-39

What effect did the expansion have on net cash flow and operating cash flow?

NCF 06 = NI + Dep = ($160,176) + $116,960 = -$43,216 NCF 05 = $87,960 + $18,900 = $106,860 OCF 06 = NOPAT + Dep = ($78,569) + $116,960 = $38,391 OCF 05 = $114,257 + $18,900 = $133,157

1-40

What was the free cash flow (FCF) for 2006?

FCF = OCF – Gross capital investment FCF 06 - OR = NOPAT – Net capital investment = -$78,569 – ($1,852,832 - $1,187,200) = -$744,201 Is negative free cash flow always a bad sign?

1-41

Economic Value Added (EVA)

EVA = After-tax Operating Income __ After-tax Capital costs = Funds Available __ Cost of to Investors Capital Used = NOPAT – After-tax Cost of Capital

1-42

EVA Concepts

 In order to generate positive EVA, a firm has to more than just cover operating costs. It must also provide a return to those who have provided the firm with capital.

 EVA takes into account the total cost of capital, which includes the cost of equity.

1-43

What is the firm’s EVA? Assume the firm’s after-tax percentage cost of capital was 10% in 2005 and 13% in 2006.

EVA 06 = NOPAT – (A-T cost of capital) (Capital) = -$78,569 – (0.13)($1,852,832) = -$78,569 - $240,868 = -$319,437 EVA 05 = $114,257 – (0.10)($1,187,200) = $114,257 - $118,720 = -$4,463

1-44

Did the expansion increase or decrease MVA?

MVA = Market value __ of equity Equity capital supplied During the last year, the stock price has decreased 73%. As a consequence, the market value of equity has declined, and therefore MVA has declined, as well.

1-45

Pure Expectations Hypothesis

Maturity 1 year 2 years 3 years 4 years 5 years Yield 6.0% 6.2% 6.4% 6.5% 6.5% If PEH holds, what does the market expect will be the interest rate on one-year securities, one year from now? Three-year securities, two years from now?

1-46

Spot and forward rates

6.2% = (6.0% + x%) / 2 12.4% = 6.0% + x% 6.4% = x% PEH says that one-year securities will yield 6.4%, one year from now.

1-47

Spot and forward rates

6.5% = [2(6.2%) + 3(x%) / 5 32.5% = 12.4% + 3(x%) 6.7% = x% PEH says that one-year securities will yield 6.7%, one year from now.

1-48

Returns

The rate of return on an investment can be calculated as follows: Return = Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.

1-49

What is Risk?

 Two types of investment risk  Stand-alone risk  Portfolio risk  Investment risk is related to the probability of earning a low or negative actual return.

 The greater the chance of lower than expected or negative returns, the riskier the investment.

1-50

Probability distributions

 A listing of all possible outcomes, and the probability of each occurrence.

 Can be shown graphically.

Firm X Firm Y -70 0 15 Expected Rate of Return 100 Rate of Return (%) 1-51

The average and the standard deviation Small-company stocks Large-company stocks L-T corporate bonds L-T government bonds U.S. Treasury bills Average Standard Return 17.3% Deviation 33.2% 12.7

6.1

5.7

3.9

20.2

8.6

9.4

3.2

.

1-52

Return comparisons

Economy Recession Below avg Average Above avg Boom Prob.

0.1

0.2

0.4

0.2

0.1

T-Bill 8.0% 8.0% 8.0% 8.0% 8.0% A B -22.0% 28.0% -2.0% 20.0% C 10.0% -13.0% 14.7% -10.0% 0.0% 7.0% 35.0% -10.0% 45.0% 50.0% -20.0% 30.0% M 1.0% 15.0% 29.0% 43.0%

1-53

T-Bills and their risk and return.

    T-bills will return the promised 8%, regardless of the economy.

No, T-bills do not provide a risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time.

T-bills are also risky in terms of reinvestment rate risk.

T-bills are risk-free in the default sense of the word.

1-54

Asset and market returns.

 A – Moves with the economy, and has a positive correlation. This is typical.

 B – Is countercyclical with the economy, and has a negative correlation. This is unusual.

1-55

Calculating expected returns.

^ k  expect ed rat e of ret urn ^ k  i n   1 k i P i ^ k A  (-22.%) (0.1)  (-2%) (0.2)  (20%) (0.4)  (35%) (0.2)  (50%) (0.1)  17.4%

1-56

Summary Calculating expected returns.

A M C T-bill B Exp return 17.4% 15.0% 13.8% 8.0% 1.7% A has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?

1-57

Risk: Calculating the standard deviation   Standard deviation   Variance   2   i n   1 ( k i  kˆ ) 2 P i

1-58

Risk: Calculating the standard deviation   i n   1 (k i ^  k ) 2 P i  T  bills        (8.0

8.0) 2 (0.1)  (8.0

8.0) 2  (0.4) (8.0

8.0)  (8.0

2 (0.2) 8.0) 2 (0.2)  (8.0

8.0) 2 (0.1)       1 2  0 .

0 %   A M  2 0.0%   B C  13.4%  18.8%  15.3%

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Risk: Calculating the standard deviation

Prob.

T - bill C A 0 8 13.8 17.4

Rate of Return (%) 1-60

Standard Deviation as a Measure of Risk  Standard deviation (σ i ) measures total, or stand-alone, risk.

 The larger σ i is, the lower the probability that actual returns will be closer to expected returns.

 Larger σ i is associated with a wider probability distribution of returns.

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Comparing Risk and Return

Security T-bills A B C M Expected return 8.0% 17.4% 1.7% 13.8% 15.0% Risk, σ 0.0% 20.0% 13.4% 18.8% 15.3% 1-62

Coefficient of Variation (CV)

A standardized measure of dispersion about the expected value, that shows the risk per unit of return.

CV  Std dev Mean   ^ k

1-63

Risk rankings, by coefficient of variation CV T-bill A B C M 0.000

1.149

7.882

1.362

1.020

  B has the highest degree of risk per unit of return.

A, despite having the highest standard deviation of returns, has a relatively average CV.

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Investor attitude towards risk

 Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities.

 Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities.

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Illustrating diversification effects of a stock portfolio 

p (%) 35 Company-Specific Risk Stand-Alone Risk,



p 20 Market Risk 0 10 20 30 40 2,000+ # Stocks in Portfolio 1-66

Breaking down sources of risk

Stand-alone risk = Market risk + Firm-specific risk  Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta.

 Firm-specific risk – portion of a security’s stand alone risk that can be eliminated through proper diversification.

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Capital Asset Pricing Model

 Model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification.

 Primary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a well diversified portfolio.

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Beta

 Measures a stock’s market risk, and shows a stock’s volatility relative to the market.

 Indicates how risky a stock is if the stock is held in a well-diversified portfolio.

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Calculating betas

 Run a regression of past returns of a security against past returns on the market.

 The slope of the regression line (sometimes called the security’s characteristic line) is defined as the beta coefficient for the security.

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Illustrating the calculation of beta See Excel file

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Comments on beta

 If beta = 1.0, the security is just as risky as the average stock.

 If beta > 1.0, the security is riskier than average.

 If beta < 1.0, the security is less risky than average.

 Most stocks have betas in the range of 0.5 to 1.5.

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Can the beta of a security be negative?

  Yes, if the correlation between Stock i and the market is negative (i.e., ρ i,m < 0).

If the correlation is negative, the regression line would slope downward, and the beta would be negative.

 However, a negative beta is highly unlikely.

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40 _ k i

Beta coefficients

A: β = 1.30

20 20 0 20 40 -20 T-bills: β = 0 _ k M B: β = -0.87

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Comparing expected return and beta coefficients Security A M C T-Bills B Exp. Ret.

17.4% 15.0

13.8

8.0

1.7

Beta 1.30

1.00

0.89

0.00

-0.87

Riskier securities have higher returns, so the rank order is OK.

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The Security Market Line (SML): SML: k i = k RF + (k M – k RF ) β i   Assume k RF = 8% and k M = 15%.

The market (or equity) risk premium is RP M = k M – k RF = 15% – 8% = 7%.

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What is the market risk premium?

 Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk.

 Its size depends on the perceived risk of the stock market and investors’ degree of risk aversion.

 Varies from year to year, but most estimates suggest that it ranges between 4% and 8% per year.

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Calculating required rates of return  k A     k M k C k T-bill k B = 8.0% + (15.0% - 8.0%)(1.30) = 8.0% + (7.0%)(1.30) = 8.0% + 9.1% = 17.10% = 8.0% + (7.0%)(1.00) = 15.00% = 8.0% + (7.0%)(0.89) = 14.23% = 8.0% + (7.0%)(0.00) = 8.00% = 8.0% + (7.0%)(-0.87)= 1.91%

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Expected vs. Required returns

^ k k PIIC 17.4% 17.1% Underv alued ( k ^  k) PSE 15.0

15.0

Fairly val ^ ued ( k  k) VOIC 13.8

14.2

Overvalued ^ ( k  k) T bills 8.0

8.0

Fairly val ued ( k ^  k) GMC 1.7

1.9

Overvalued ( k ^  k)

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Illustrating the Security Market Line

SML: k i = 8% + (15% – 8%) β i k i (%) SML -1 k M = 15 k RF = 8 .

T-bills .

B 0 1 .

A .

C 2 Risk, β i 1-80