Managerial Finance

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Chapter 11

Introduction to Risk, Return, and the Opportunity Cost of Capital

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Topics Covered

11.1 Rates of Return: A Review

11.2 A Century of Capital Market History

11.3 Measuring Risk

11.4 Risk & Diversification

11.5 Thinking About Risk

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2

Rates of Return

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5

Rates of Return

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6

Rates of Return

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8

Rates of Return

Nominal vs. Real

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11

Market Indexes

Market Index — Measure of the investment performance of the overall market

Dow Jones Industrial Average (The Dow) — Index of the investment performance of a portfolio of 30 “blue-chip” stocks

Standard & Poor’s Composite Index (S&P 500) — Index of the investment performance of a portfolio of 500 large stocks, also called the S&P 500

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12

The Value of a $1 Investment in 1900

Source: Ibbotson Associates

Year Start

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13

Equities 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 1 1.2423159767536101 1.4657087030686597 1.5544806713254955 1.328021585933117 1.7016017 105677075 2.0769426699571247 2.1615414004935678 1.5283943407437852 2.2443693120803201 2.6933648536268566 2.4640273958001306 2.6038113668933773 2.7908980653502748 2.5732420116924088 2.4307433259031552 3.3735092316599706 3.5895957595030694 2.9106725852004827 3.4815417154196462 4.2001394672627423 3.4493430157528797 3.8495536874555949 5.0286002020371932 5.1790869012554497 6.5791803581643933 8.4408992766044211 9.2204164632217491 12.299142471779964 17.078120247999895 14.592997254090902 10.428773017463852 5.8883299495775558 5.3764685246107558 8.445991866950779 8.8075497018091102 12.710770300089138 16.811378168783182 10.979350068887369 14.063029746674443 14.465191633064549 13.441759561162426 12.092899631043506 14.032776524527184 18.015813642549077 21.854125935943038 30.174010189732353 28.406866426440814 29.423658170498381 30.044346787019194 36.11863144231711 46.813542825149497 56.495411247260819 64.075081130248307 64.505331937305414 96.743720588733098 121.13695774315535 131.14865414406174 117.96475906668462 171.07484321663418 192.74777229093004 194.98060932767117 247.51968950381087 222.33335768554812 268.97436813316807 312.34899541704976 357.52464232463075 326.27604060024998 420.04137294167782 479.44162448328041 427.11711893877333 427.12697718085673 502.64302670470948 593.01882385957333 483.21729185445622 346.04119188654187 479.17239937841003 606.57156290583453 590.57565754320478 645.35042110549341 810.31540224342996 1083.1470303704398 1042.5315260838181 1237.5918740326601 1528.0040483723892 1574.5651600803974 2087.3140110182717 2423.2664638232682 2478.3829291704164 2923.0434686226417 3775.8067501445689 3542.424569894727 4754.0898368849821 5180.4138153199474 5764.83884406995 5761.114296744373 7860.9602133674953 9528.3656948249554 12509.899931590146 15441.08871001899 19078.899274448278 17000.418249659495 15134.787409948956 11977.712528825306 15767.541858799965 17735.127905295183 18866.010648897092 21841.817112116762 23068.290871637029 14478.869868533558 18576.978092665675 21765.600572985219 21978.143228107579 25507.220079410268 Bonds 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 1 1.060824918307623 1.1066260016025602 1.1114007221741922 1.125534082654583 1.130869657975812 1.1598927892229782 1.2004883458038909 1.1368705624725528 1.1941861391306032 1.1740555118430067 1.210272726887635 1.2341114116879839 1.2766516539066806 1.3097257625988179 1.3272890395461687 1.3839794874761711 1.4395211635351635 1.3916569019189504 1.4545953839337631 1.5162178672616391 1.4308541969947666 1.5527291234678107 1.705946527238198 1.7691822957112731 1.9498323485256364 2.055969935164256 2.2157062458571084 2.4135216946657656 2.4160303386222126 2.4986900812613411 2.6150896482253176 2.4762443245812817 2.8933001230176725 2.8911557120145019 3.1810217845989444 3.3395665961652305 3.5905421573244785 3.5988709041431628 3.7979715960258504 4.0235678214646704 4.268478092829719 4.3082949285165206 4.4469424065644541 4.5396296883753733 4.6674054319669303 5.1684218372680375 5.1631638026104367 5.0277302380894042 5.1986085927604915 5.5338504993255171 5.5371277240003218 5.3194442023283193 5.3811620577045396 5.5768701639249407 5.9776938584437707 5.9004238008777037 5.5707954886035314 5.9862887684807333 5.6215012178294854 5.4946075194172739 6.2516870336064763 6.3125433121936183 6.7472681004479051 6.8291237457501692 7.0685630312546897 7.1187290954439701 7.3786898072518445 6.701243742986331 6.6838035321052987 6.3446890691501556 7.1127721530317247 8.0537698761742913 8.5117065989567529 8.4174995713931846 8.7840411114631358 9.5918141012772953 11.198914021915733 11.121841930630371 10.990890158117985 10.855260331276217 10.426843265825413 10.620547631915183 14.907143315372711 15.004301205853801 17.326507329388729 22.69197340506846 28.258506021224523 27.491551154372434 30.150810553868219 35.612519447280349 37.814267241828119 45.112182581266246 48.745460457832003 57.636844312804627 53.158237371376714 69.992572442458282 69.340696542947114 80.334070422653085 90.827966317752626 82.686373206173556 100.44655974430503 104.15856156231051 122.73945393624898 124.51702985982838 135.11314255316069 145.66865096011659 147.40008762373628 161.96684998906838 203.87230739756663 173.48862144487376 191.08671908603279 245.03683584562216 253.14050430377074 Bills 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 200 5 2006 2007 2008 2009 2010 2011 2012 2013 1 1.0477748038267189 1.0940443250630152 1.1478763103054186 1.2143857149000927 1.2713653684493413 1.3252138930882078 1.4027219835539986 1.4912888146562502 1.5713931986523686 1.6302632013481753 1.713568483436376 1.7865435139677748 1.8700060990556475 1.9820687738960077 2.0834707300822903 2.1608811877145162 2.2331316792292579 2.3365352662916039 2.4753953489961864 2.6150197569971478 2.8045619691807664 3.0067372151592071 3.1453439599737618 3.3029720889901086 3.4420887842909966 3.5773298864759835 3.6941816502812186 3.8096145019621894 3.9451566714344555 4.1324734074220757 4.232 0800958110842 4.2774914393023513 4.3186292690956218 4.3314753987014916 4.3385276077688051 4.3458436480263964 4.3535549832203779 4.3669604587617359 4.3662520688596569 4.3671471248154248 4.3673566560724 4.3699644481013156 4.3816770351285967 4.396888068974059 4.4114197513871209 4.4259596292638586 4.4415863634628714 4.4639469611672871 4.5001574011183409 4.5497775757038479 4.6041745971526788 4.6729060041235488 4.7502899196014567 4.8369218370142857 4.8787072050149032 4.9554812315084567 5.0773486746379017 5.2367293866330842 5.3174520722387495 5.4744214643568787 5.620191015492332 5.7397058544232387 5.8966083736648383 6.0803773486865689 6.2953624063406641 6.542596085519401 6.8539786247162215 7.142531654078482 7.5143571121263264 8.0090878955123479 8.5316785183035506 8.905888864100147 9.2478707778149118 9.888777285128926 10.680181950014862 11.300016420201322 11.874341566545857 12.482332967753178 13.378667237980702 14.766868546994557 16.426001789657093 18.842079823026218 20.828616406210276 22.661185200564042 24.893173106133599 26.815746348841621 28.468249102244965 30.024208491507025 31.930087042100951 34.602771399999739 37.306448500787013 39.393845127024193 40.775114288582706 41.956347335891842 43.594096606366534 46.033381977323515 48.430371485087804 50.975651375229852 53.450980750541383 55.954542332228399 59.252068247234391 61.5189076280055 62.531930172963499 63.17066043902328 63.930327379331743 65.835154181166672 68.994987868942331 72.211696132153861 73.366464150618981 73.437454424597647 73.526590207796616 73.5572780098571 73.601181335233278

Dollars

Expected Return

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Rates of Return

Common Stocks (1900-2013)

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1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 24.231597675361005 17.981957126464245 6.0565901035437353 -14.56815060937865 28.130576233977344 22.058097206789462 4.0732337854173739 -29.291461158468181 46.844911175744699 20.005421528881961 -8.5149049716715002 5.6729877001978402 7.185109521973998 -7.7987819175527218 -5.5377102169854915 38.785086673292653 6.4053931086108573 -18.913638743449333 19.612962760627472 20.640216621861729 -17.875512405285942 11.6025187948831 30.628135371217603 2.992616099352885 27.033596531650204 28.297125433409633 9.2350016399071357 33.390313993284224 38.856186821033731 -14.551501908999843 -28.535770713310317 -43.537653569436642 -8.6928115331499463 57.091812744542203 4.2808214896951302 44.316759262548231 32.260891919864896 -34.69095776291099 28.08617685417849 2.8597101309922657 -7.0751366304941392 -10.034846434957901 16.041453684969387 28.383813503052234 21.305239771845663 38.070084697854554 -5.8565094668552415 3.5793872115058356 2.1094882659530967 20.217729140053532 29.610511128896412 20.681768218811158 13.416434566364877 0.67147914519611884 49.977866454142259 25.214284716338597 8.2647745060050237 -10.052634671260229 45.02199179665751 12.668682704476408 1.1584243024977292 26.945797511508474 -10.175486188089689 20.977963420849122 16.125933331464172 14.463195838764342 -8.7402651524107196 28.738037941409299 14.141523994554284 -10.913634292996555 2.308088729363611E-3 17.679999990231778 17.980115579710887 -18.515690832626596 -28.388077637178476 38.472647364917911 26.587333430032434 -2.6371011008165191 9.2748088856475555 25.562078483709595 33.669806518751997 -3.7497683276416338 18.710258929201864 23.465908304118766 3.0471851012177975 32.564473286814845 16.094964678606559 2.2744698600000168 17.941559160152277 29.173814576344803 -6.18098847990316 34.204405572600891 8.9675204521230789 11.28143522090248 -6.4608004253374762E-2 36.448607135077204 21.211218937631205 31.291139868661013 23.430953040855051 23.559288031736301 -10.89413490207175 -10.974029063949098 -20.859723996178005 31.640676972787052 12.478711419415678 6.3765130403387715 15.773374236877347 5.6152551466969403 -37.23475246128595 28.304061445005434 17.164376597819398 0.97650719266695329 16.057211087738278 33.06

Year

Rate of return (%)

Expected Return

Expected market return = interest rate on Treasury bills + normal risk premium
(1981) 21.6% = 14 + 7.6
(2014) 7.7% = .1 + 7.6

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Expected Returns

1900-1926 1927-1955 1956-1983 1984-2013
Stocks 11.0% 11.6% 11.0% 12.4%
Treasury bills 4.9% 1.0% 5.6% 4.0%

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Country Risk Premiums (%)

Country risk premiums (1900-2013)

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Measuring Risk

Variance

Average value of squared deviations from mean

A measure of volatility

Standard Deviation

Square root of variance

Another measure of volatility

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Histogram of Returns

% Return

Number of Years

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Measuring Risk

Coin toss game calculating variance and standard deviation

Expected return = (.25 × .40) + (.5 × .10) + (.25 × −.20)

= .10 of 10%

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Risk and Diversification

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Stock Market Volatility 1900-2013

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Standard Deviations

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Portfolio rate of return = fraction of portfolio in first asset × rate of return on first asset
+ fraction of portfolio in second asset × rate of return on second asset

Risk and Diversification

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