1. Chapter One  Introduction of Portfolio Theory

2. Part One The asset classes

3. Basic principles  There are many asset classes and many of them are useful to investors.  Some asset classes are noted for their long term stability (low risk), others for their high returns.  Generally speaking, the higher the reward you are after, the more risk you ’ ll need to take.  Portfolios can be constructed that exhibit superior risk and return relationships to any single asset, because one can significantly reduce risk by diversification.

4. Why risk and return are linked

5. When two investments appear to offer identical risk, investors will prefer to buy the higher returning one. If the market is peopled by reasonably well informed investors, there simply won’t be any high returning low risk investments left and nobody will buy high risk assets with a low expected return.

6.  In a portfolio construction context “ risk ” is usually measured with some sort of measure of price volatility.  There are other risks of course that need to be taken into account.

7.  Inflation risk is a major problem with the more “ conservative ” asset classes such as fixed interest and cash. Many pensioners find to their horror that they can no longer live off their savings, despite the conservatism of their strategy, simply because inflation devalued their money and the portfolio did grow enough to keep up.  It is necessary for all but the most short term oriented investors to consider at least some exposure to growth assets like shares and property, just to fight inflation.

8. Major asset classes: shares  Shares are part interests in businesses. How good a return you get on your share depends to a large extent on the fundamental business developments of the company itself and on the price you paid for the share.

9.  Averaged out over many companies, shares as an asset class tend to respond to interest rates and the economy.  Although in the last few years many markets have fallen substantially, shares are still the highest performing asset class over the long term.

10.  Shares generally go up in price over the long term because businesses don ’ t pay out 100% of their profits as dividends, they keep some to grow the value of the business itself.  Over the long term, shares have beaten inflation.

11. Major asset classes: property  There are many types of property to invest in, each are different.  The highest income yield comes generally from commercial and industrial property.

12. Major asset classes: fixed interest  A “ fixed interest ” investment is a debt that can be bought and sold.  The borrowers are usually governments and companies. A typical fixed interest investment pays a regular “ coupon ” (interest payment) and will repay the principle on maturity.

13.  Some fixed interest securities have a maturity of several decades, others are shorter term.  The actual price of a fixed interest investment will fluctuate in response to many things, most particularly interest rates. If general interest rates fall, the price of a long term fixed interest security will usually rise such that the “ yield to maturity ” is similar to those of other investments with a similar risk. On the other hand, if interest rates rise, fixed interest investments fall.

15. Major asset classes: cash  “ Cash ” may mean currency, but in an investment context cash is just a really short term highly liquid fixed interest investment.  Longer term fixed interest investments are usually called “ bonds ”, shorter term fixed interest investments may be called “ notes ” and really short term ones are often called “ bills ”.

16.  Cash management trusts usually invest in a portfolio of high quality short term fixed interest investments. Because of the short maturity, these fixed interest investments are not as sensitive to interest rate changes and thus don ’ t have a great deal of capital volatility.

17. Other asset classes  Shares, property, bonds and cash are the major asset classes, but there are many others to choose from.

18.  Hedge funds are sometimes called a distinct asset class as they pursue unconventional strategies that give them performance very different to the asset classes that they invest in.

19.  “ Private equity ” is basically a shares investment, but in companies not listed on a stock exchange.  Agribusinesses are agricultural investments in things like tree farms and vineyards.

20.  Some people also consider commodities like gold to be an asset class of its own, and many people consider collectibles, race horses and fine wines to be useful alternative investment asset classes.

21. The point of portfolio construction  A portfolio is often more than the sum of its parts. Because not all asset classes perform the same way over the short term, a portfolio of many asset classes usually offers a superior overall relationship between risk and return to any single asset

22.  A portfolio consisting only of shares would have done badly in the last few years since the market crashed, but property has performed very well. This is quite typical, more “ defensive ” asset classes often do well when equities are falling.

23.  A diversified portfolio has a reasonable long term growth rate because over time all asset classes offer a positive return, but being invested across different asset classes smooths out returns and offers a more predictable growth rate.

24. Part Two Creating diversified portfolios

25. How diversification reduces risk There are two mechanisms by which diversification reduces risk: dilution and interference. There are two mechanisms by which diversification reduces risk: dilution and interference.  Dilution is easy to understand, if you swap half your shares for cash then you lose half your equity exposure and therefore half your equity risk. If the market crashed tomorrow you ’ d only lose half as much

26.  “ Interference ” is where negative movements in some assets are partly cancelled by positive ones in other assets. A good example is with property vs. shares, in the recent bear market in shares property did very well while shares did badly, the opposite may be true in the next few years.

27. Interference and correlation “Correlation” is the word given to the extent to which assets move together, this is measured with statistical formulae. Correlations can range from -1 (perfectly negatively correlated) through to +1 (perfectly positively correlated).

28. If asset B tends to move in the opposite direction to asset A then these two assets are said to have “negative correlation”, and they can be highly effective at cancelling out each other’s volatility. If the assets both trend upwards over the longer term a combination of them will have a return equal to the average of the two assets’ returns but with substantially reduced volatility.

29. the greatest Negatively correlated assets cancel most amount of each other’s volatility.

30. Negative correlation isn ’ t essential  Assets don ’ t need to be negatively correlated to have some volatility smoothing.  As long as the correlation is less than +1 the assets will be at least a little bit different and at least some volatility will be cancelled.

31.  Most real world assets are positively correlated because most prices are related somehow to important “ macro ” factors like global economic growth, interest rates, oil prices etc.  Even if negative correlations are rare, substantial volatility reduction is possible by using assets with a low positive correlation.

32.  The “efficient frontier” is the name given to the line that joins all portfolios that have achieved a maximum return for a given level of risk (portfolios that are “efficient”). If you chart every possible portfolio that could be constructed out of a group of assets and plotted a point on a risk vs. return chart, the resulting plot usually looks much like the chart in next slide. The top of the curve is the efficient frontier, anything below that curve is an “inefficient” portfolio, anything actually on the curve, or close to it, is an “efficient” portfolio

34. Efficient vs. inefficient portfolios  It is impossible to predict in advance which portfolios will be the most efficient as this would require knowing in advance asset class performance and correlations  A portfolio that has been diversified into a variety of asset classes should be close to efficient over the longer term, provided it is rebalanced regularly.

35. Rebalancing  Rebalancing a portfolio is the process of adjusting a portfolio to bring it back to its original asset allocation.  Since assets perform differently at different times, the portfolio is likely to drift from your desired asset allocation.  Failure to rebalance means that a portfolio can change risk profile over time and may no longer be appropriate.

36. A few simple rules of portfolio construction  If you have two assets with roughly equal expected returns, putting 50% into each is a way to hedge one ’ s bets (and spread the risk) without compromising expected return at all. The lower the correlation of those assets, the more the risk will be reduced

37. If   1  Mean of X 1 Mean of X 2 Where P = ½ [X 1 ] + ½ [X 2 ]  1,2  1/2  1 + 1/2  2

38. If  = 1  Then all the portfolios are here

39. If   1   Then all the portfolios are here

40. This Means the “ boundary ” of the possible portfolios looks like this 

41.  Standard Deviation Mean Maximizes Utility

42. Combine with Risky Assets  Mean Standard Deviation Risky Assets Risk Free Asset ?

43.  Mean Standard Deviation Risk Free Asset

44.  Actually, this holds true with a greater number of investments. If you have 5, 10 or 1,000 assets  There is such a thing as “ diversifiable ” risk, as you add extra assets to the portfolio the volatility tends to decrease – but only up to a point. When a portfolio reaches a certain level of diversification the only way to reduce risk is to add lower risk assets which will reduce volatility by dilution, this usually reduces the return

45. Diversification can also increase returns A higher return may often be obtained from rebalancing the portfolio as a result of “ reversion to the mean ”. If you believe that at some point in the future two assets will give the same cumulative return then it would make sense to invest in the asset class with the worst recent performance and sell the one with the best performance!

46. Rebalancing does precisely this, although it is normally seen only as a risk management technique. This is why the diversified portfolio did a little better than all three component asset classes. A small “ rebalancing premium ” is quite common because last year ’ s worst performing asset class often outperforms last year ’ s best performing asset class this year.

47. Pushing out the efficient frontier  Investors desire higher returns with lower risk. There is however a limit to what can be achieved with a particular set of assets, that limit is drawn on charts as the efficient frontier.  By adding more assets we can change the shape of the efficient frontier. Assets carry two items of interest to us, their returns and their correlation with the rest of the portfolio.

48. Refining our asset allocation  There is wide acceptance that so-called “ value ” stocks outperform “ growth ” stocks, and “ small companies ” tend to outperform “ large companies ”, at least over the longer term

49.  Their higher long term performance is very interesting, but so too is the fact that they often have a low correlation to large growth companies, the dominant stocks in the market.  They provide what asset allocation is independent source of risk and return. This may enable us to improve the efficient frontier. This may enable us to improve the efficient frontier.

50.  The stock market is dominated by what would be classified as “ large growth companies ”, also known as “ blue chips ”. 蓝 筹 As a portion of market capitalisation, the very largest companies dominate the market and so an exposure in market weightings tends to have a very small amount of small company and value exposure

51.  Many asset allocators believe a portfolio should have more small company and value exposure than the market gives. Although small companies might only make up 5% of the market by capitalisation, they make up the vast majority of listed companies by number, despite the tiny market weighting, asset allocators often allocate a larger amount of 10 to 20% to small caps.

52.  A non-technical approach goes back to the basics – try to build your portfolio from many “ independent sources of risk and return ”. This simply means you should diversify into many different asset classes

53. how do you go about constructing a portfolio?  The usefulness of historical correlations and returns is usually overstated, but can form a crude guide as long as we don ’ t take them too seriously.  Don ’ t get too hung up on quantitative data, but try to find assets that are very different (i.e. property vs. shares.)

54. Decisions  Active funds or passive/index funds?  How much to growth assets, how much to income assets?  Balance of value stocks to growth stocks?  How much large cap shares, how much small caps?  How much money to put in developed markets vs. emerging markets?  Listed or unlisted property?  Short or long maturity fixed interest?

55. Risky assets vs. risky portfolios.  It is important to think about risk in a portfolio context, not an asset context.

56.  Small percentage allocations to riskier assets like emerging markets, private equity, commodities, hedge funds and agribusiness can actually reduce the risk of the overall portfolio because they don ’ t operate on the same cycles as major asset classes. Small allocations to such assets can have a great impact on the efficient frontier.

57. Are risky assets like emerging markets too risky for conservative portfolios?  Emerging markets are by themselves a very risky asset class, their monthly volatility is about 50% higher than global large companies. On the other hand, their correlation with the global large caps indexes is quite low.

58.  Despite the high volatility of emerging markets, their low correlation with global large cap equities means a small percentage allocation of emerging markets to a global portfolio can actually reduce the volatility of a portfolio while potentially increasing returns.

59. A little volatility can go a long way  In a sense, the high volatility of the riskier asset classes is one of their most valuable attributes for a portfolio.  The high volatility of asset classes like emerging markets and commodities means they do well above their weight in contributing risk and return to the portfolio.

60. Some notes  Obviously some asset classes have been more efficient than others over this time frame, but which asset classes will be best over the next 10 years is another matter entirely.  There really is no way to forecast which assets are going to outperform, although it doesn ’ t stop people from trying!

61. Adding conservative assets  So far we ’ ve only shown what happens when growth assets of the various flavours of shares and property are added together.  Although we can substantially improve on large cap growth share portfolios in terms of risk and return there are limits to how conservative a portfolio of growth assets can be, to push the efficient frontier more toward lower risks the income asset classes (bonds, cash, mortgages) will need to be added.

62.  We have to accept that over the longer term this will probably cost the investor money due to a lower expected return, but the risk reduction potential is tremendous and this may be more suitable for conservative investors.

63. Half the risk doesn ’ t mean half the return!  Risk to reward ratios get more favourable for conservative portfolios.  Putting half a share portfolio into cash will basically halve the risk, but since cash doesn ’ t return 0% you won ’ t halve the return.

64.  If you gear a portfolio though you do double your risk (if you use 50% gearing), but because you have to pay interest on the loan you won ’ t double your return.  Conservative portfolios therefore can greatly reduce risk without necessarily having the same amount of reduction in the return. This can be seen on the efficient frontier, which is usually curved instead of straight.

65. Part Three Risk profiling and portfolio design

66. why not always use a medium risk portfolio?  If diversification makes it relatively easy to substantially reduce risk for only a small cost in return, why not do it all the time?  The answer lies in compounding interest. Over a long period a small increase in returns makes a big difference to the final portfolio value.

67.  The difference between a portfolio that returns 8% over 20 years and a portfolio that returns 10% over 20 years is very substantial. Ten thousand dollars invested at 8% for 20 years will grow to $46,610, one thousand invested at 10% for 20 years will grow to $67,275 - a very significant difference! If you are young then your time frame on retirement assets is likely to be 30 years or more.

68.  Over a short period of time there is very little difference so it may not be worth taking a risk, but if you do have a long term horizon then serious thought should be put into ways to get an extra percentage point or two out of the portfolio. An extra point of risk is often hard to notice, but an extra point of return makes a very big difference in the long term! Risk is important but being overly conservative can be a costly mistake over the long term.

70. Choosing a level of risk vs. return  “ Risk profiling ” is a tricky business that depends on the time horizon, risk tolerance and return requirements of an investor.  Some model portfolios with different levels of risk and their risk/return profiles are shown on the next few slides.

71. Three dimensional approach to risk profiling Most advisors discuss risk tolerance in terms of potential volatility only, often using short multi-choice questionnaires. In my opinion, this is inadequate and doesn ’ t really address the client ’ s needs. there are actually three dimensions to risk profiling:

72. 1.Time frame – when is the money required? 2.Volatility tolerance – how much volatility? 3.Conventionality – given the different cycles of value and small cap shares and that they may underperform large growth companies for extended periods of time, how much of a value and small cap tilt is acceptable?

73. Designing a portfolio – risk tolerance  Examining data from model portfolios and adding on a margin of safety, decide how much downside risk over that time frame that you can accept.  First, determine the time frame of the investment.

74.  Remember, the consequence of risk is more important than the probability of risk. Risk should be assessed in terms of how much damage it would do to your ability to pay for something you need at some time in the future. Don ’ t get too obsessed about daily, weekly, monthly or even annual volatility if your investment horizon is 20 or 30 years!  Of course if your investment horizon is quite short term, you probably should be obsessed about short term volatility!

75. Designing a portfolio – value vs. growth  Value stocks and small companies tend to outperform large cap growth companies over the longer term but they do have risks of their own.  Value stocks outperformed by a huge margin during the “ bear market ” of the last few years.

76.  The trouble though is that during the “ tech boom ” of the late 1990s, value stocks lagged by a large margin. We know with hindsight this was a bubble, and most of those gains were lost, but this wasn ’ t that easy to spot at the time. The newspapers were all touting the “ new economy ”, and value investors seemed like they were obsolete. As a dimension to risk profiling, this one is about how willing you are to ignore underperformance and the prognostications of experters.

77.  Some people are happy to have a very strong tilt toward value stocks, but not everyone feels that way.  The numbers for value vs. growth strongly favour value for more than half a century in the US and many other markets where data is available, the track record of value is impressive.  But how many years will you persist with value investing if it underperforms the general market? How do you know there isn ’ t really a “ new paradigm ” and markets haven ’ t really changed

78.  Most people prefer to hedge their bets, allocating some but not all of their portfolio to value stocks, buying growth stocks and having a “ balanced ” exposure. This may not be the highest returning strategy for the very long term, but it seems more conservative for most people.

79. Is value more risky than growth?  Many academics argue that the outperformance of value stocks vs. growth stocks is a “ risk premium ”, i.e. that investors are merely being rewarded for taking on more risk.

80.  Others who don ’ t believe in the “ efficient market hypothesis ” think that the outperformance of value is caused be systematic errors made by analysts who overestimate the future profits of “ growth stocks ” and underestimate the future profits of “ value stocks ”, this would be an “ inefficiency ”, an opportunity to earn a higher return without higher risk.

81.  Various people have put forward various theories about the extra risk of value, but one of the most obvious troubles in the value = risky theory is that value based portfolios tend to be less volatile, not more.

82. Risk of value stocks  The main reason why many academics say value stocks are more risky is because in theory they would have to be more risky for the efficient markets hypothesis to remain valid. Many explanations are given, but some tend to be almost metaphysical, claiming that the risk can ’ t be measured but is there somehow and somewhere

83.  Interestingly, prior to academics discovering the “ value premium ”, nobody claimed value stocks were more risky, this claim was made by efficient market supporters only after the higher returns were documented.  It is an interesting issue, but from a personal investor ’ s point of view it is a question of whether the value premium is likely to persist for ever and whether they are willing to tolerate periods of underperformance where growth does better than value.

84. Value vs. growth In the late 1990s, growth stocks outperformed value stocks. If you had switched out of value and into growth following that period of outperformance you would have been hurt badly by the bear market that followed, where value stocks outperformed growth by a big margin. In the late 1990s, growth stocks outperformed value stocks. If you had switched out of value and into growth following that period of outperformance you would have been hurt badly by the bear market that followed, where value stocks outperformed growth by a big margin. Growth stocks often outperform in rising markets, especially in the latest stages of bull markets when most people invest the most money. Typically, value stocks offer more consistent performance. Growth stocks often outperform in rising markets, especially in the latest stages of bull markets when most people invest the most money. Typically, value stocks offer more consistent performance. If you can ’ t tolerate underperforming the market or don ’ t want to bet on a value premium continuing, stick with normal large cap “ blue chip ” shares. Strongly tilted value and small cap portfolios aren ’ t suitable for everyone. If you can ’ t tolerate underperforming the market or don ’ t want to bet on a value premium continuing, stick with normal large cap “ blue chip ” shares. Strongly tilted value and small cap portfolios aren ’ t suitable for everyone.

85. Part Four  Starting and managing a portfolio

86. The importance of rebalancing  Rebalancing consists of regularly adjusting the portfolio to re-establish the original asset allocation.  If you don ’ t rebalance, periods of high performance for some assets and/or low performance for others will mess up the asset allocation.  If the market reverses then such a portfolio might experience greater losses or be less exposed to the recovery in underperforming assets.

87.  Apart from anything else, if you don ’ t rebalance then the portfolio will drift towards other risk profiles, resulting in a different risk and return profile to what it was intended for. A balanced portfolio will become high growth by the end of a bull market, a high growth portfolio will become a balanced portfolio near the market bottom – the opposite of what one should be doing.

88. Rebalancing and capital gains tax  Obviously any time one sells an asset at a profit a capital gains tax liability will be created. If you are rebalancing then it is quite likely that a higher than normal proportion of capital gains will be realised because we are necessarily selling the best performing assets.

89.  For tax reasons it is usually a good idea to implement rebalancing first by buying underperforming asset classes with new contributions and reinvestment of income, thus minimizing sales.

90. Approaching retirement  The closer one gets to retirement, the more appropriate it is to start implementing a conservative investment strategy since withdrawals will start soon.  This need not always involve selling high growth assets. Over a number of years one can turn a portfolio from “ high growth ” into “ conservative ” by simply investing new contributions and distributions into conservative income assets

91.  If the portfolio is producing 5%pa distributions, then simply by reinvesting distributions into income producing assets the portfolio can drop a risk profile category (High Growth -> Growth -> Balanced -> Low Growth -> Conservative) about every three years. With new contributions one can change the portfolio more quickly.  It is better to gradually transition the portfolio as you approach retirement than to make a sudden change because otherwise retirement incomes can be highly susceptible to the behaviour of the market in the year or two prior to retirement.

92. After retirement  A sixty year old usually has at least another 20 years of life expectancy so unless you are planning on spending your all money within a few years at least some of your funds will have a time horizon exceeding a decade.

93. Four ways to start a portfolio 1.Contribute lump sums at your discretion 2.Dollar cost average 3.Contribute a single lump sum 4.Value average

94. Contribute a single lump sum  If you have money to invest, single lump sum investing gets that money to work immediately in the market. The trouble though is that you never know what the market is about to do and you risk making a major investment just before a market fall.

95. Lump sum investments at your discretion  Many people prefer to spread out their investment into several parcels, but incorporate market timing into their decisions.  Great caution should be exercised with this approach, various studies have shown that people are bad market timers.

96. Dollar cost averaging  If you have trouble pulling the trigger when it comes time to buy in gloom and sell in boom, consider using a mechanical approach to remove emotion from the equation.  If you invest regular amounts every month (or quarter) without fail, irrespective of what the market does and not varying the amount invested, timing mistakes are avoided

97. Dollar cost averaging as insurance  Dollar cost averaging is a way to provide an insurance policy against short term volatility following the initial investment.  If the market falls after you start your investments then your continuing regular investments will take advantage of those falls.

98. Dollar cost averaging in a volatile market  To an extent, dollar cost averaging is a way to benefit from market falls.  If the price drops, then your regular monthly contribution will buy you more shares.  In fact, if you are dollar cost averaging the best kind of market is one where the stock market only goes sideways or even down for some time.  As long as stocks eventually go up (and eventually they will), bear markets are best seen as a welcome buying opportunity, not a disaster.

99. Special needs of a pension portfolio  one could construct a pension portfolio with short term, medium term and long term components.  The reason why one would want to do this is so we know that the pension payments for the next few years are not held “ hostage ” to market volatility.  Volatility may or may not be a serious concern to investors in the accumulation phase, but it is more serious during the pension phase.

100. Dollar cost averaging in reverse  If you are dollar cost averaging during accumulation, you welcome a fall in stocks because it means you get to buy more stocks with your dollars at lower prices.  During a pension phase you dollar cost average in reverse, a bear market is more serious because a fall in stocks means you are forced to sell more stocks at lower prices in order to make up the payment.  Capital can be severely reduced by these large sales to make pension payments.

101. Pension fund withdrawals  Segregating the portfolio into short/medium/long term components is one way to reduce the impact of volatility, putting several years worth of payments into cash and low risk investments does free the pensioner from worry about stocks for at least a few years, but how does one transfer money between the portfolios to top up money that is spent?

102.  Regular fixed dollar transfers from a long term portfolio to a short term portfolio will result in dollar cost averaging in reverse – not a good thing in a volatile market.  A simple way to overcome this difficulty is to not make fixed dollar transfers, instead make percentage transfers in and out of a reserve account. (Thus you ’ ll make larger withdrawals when your portfolio is large, smaller ones when it is small).

103. Conclusions  Asset allocation is an overlooked and underrated field of investment, but studies show it is more influential on the behaviour of a portfolio than stock selection or market timing, more importantly you can exercise more control over asset allocation whereas the others are often a matter of luck

104.  Used properly, asset allocation is the major risk management tool, but it can also be a source of higher returns.  Asset allocation can be a complex area with many fine points that are often overlooked and is particularly important for pension portfolios

105. Part Five Capital Asset Pricing Model (CAPM) (CAPM)

106.  One Factor (beta-pricing) Model –Factor –Beta  Deriving the CAPM –Expected returns are linear in beta –Diversifiable and Non-diversifiable risk

107. One Factor (beta-pricing) Model  To determine the optimal risky portfolio, we need estimates of –The expected return on each security –The variance (standard deviation) of each security –The correlation between each possible pair of securities under consideration

108. Our Portfolio Problem  If we are looking at 150 to 250 securities, we need estimates of 150 – 250 expected returns and variances, but 11,175 – 31,125 correlation coefficients!

109. Is There an Easier Way?  Casual observation shows that securities tend to move together: when the economy and the market do well, most security prices increase; when the economy and the market do poorly, so do most securities.  Implication: Security prices move in response to some common (macro) factor(s).

110.  Factor Models: Statistical models designed to measure the systematic (macro) risk of a security, vs. its firm-specific risk.

111. The Single Index Model  Index Models: Factor models where market indices (portfolios) are used to proxy for the common or systematic risk factors.  The most common model is the single or market index model.  In the single index model, a broad market index (e.g., the S&P 500) is typically used as the market index.

112. Specification of the Single Index Model

113. What is Beta?  Beta: Sensitivity of a security ’ s return to the systematic or market factor  Beta measures the change in expected return for a security given a change in the return on the market

114.  Risk premium format: R i - R f =  i + ß i (R m - R f ) + e i

115. More on Beta  Beta is the slope in a regression of a security i ’ s excess return on the market excess return.  From statistics, we know that

117. Components of Risk  Using the risk premium version of the single index model,  We can write  i 2 =  i 2  m 2 +  2 (e i )  Total risk = Systematic risk + Unique Risk

118. Estimating Correlations  Importance of the single index model: we can use regression analysis to get estimates of alpha and beta.  We can use our betas to get estimates of the correlation between securities

119.  The model gives us all the inputs needed for the selection of optimal risky portfolios.  For covariance and correlation:

120. Capital Asset Pricing Model (CAPM)  Why The Market Portfolio?  We ’ ve been talking about a single Index. We explicitly used the market portfolio as such.  Is there any reason we believe that the market portfolio is a risk factor?

121. We have to Think:  What happens if all investors seek portfolios of risky securities using the framework we previously discussed?  How will using this framework affect equilibrium security prices and returns?  How does optimal diversification affect the market price of securities?  Can we develop a model that explains security prices under conditions of market equilibrium?  Can we identify a common (macro) Risk Factor?

122. CAPM: Introduction  Equilibrium model that –predicts the relationship between risk and expected return –predicts optimal portfolio choices –underlies much of modern finance theory –underlies most of real-world financial decision making

123.  Derived using Markowitz ’ s principles of portfolio theory, with additional simplifying assumptions.  Sharpe, Lintner and Mossin are researchers credited with its development.  William Sharpe won the Nobel Prize in 1990.

124. Assumptions 1.No transaction costs, 2.Assets are infinitely divisible, 3.No taxes, 4.Individuals are price takers, 5.Individuals are rational mean variance maximizers, 6.Short selling allowed,

125. 7.Unlimited lending and borrowing at the risk free rate, 8.Homogeneous expectations, 9.Single-period model, 10. All assets are marketable.  Assumptions are unrealistic. Some can be relaxed and still CAPM holds. CAPM is broadly used. It does an amazing job in practice.

126. Deriving The CAPM. Step 1: What is the Equilibrium Tangency Portfolio?  Recall from portfolio theory: –All investors should have a (positive or negative) fraction of their wealth invested in the risk-free security, and –The rest of their wealth is invested in the tangency portfolio. –The tangency portfolio is the same for all investors (homogeneous expectations).

127.  In equilibrium, supply=demand so: –the tangency portfolio must be the portfolio of all existing risky assets, the “ market portfolio ” !!

128. The Market Portfolio  p i = price of one share of risky security i  n i = number of shares outstanding for risky security i  M = Market Portfolio. The portfolio in which each risky security i has the following weight:

129. In words, the market portfolio is the portfolio consisting of all assets (everything!).

130. The Capital Market Line (CML)  Recall: The CAL with the highest Sharpe ratio is the CAL with respect to the tangency portfolio.  In equilibrium, the market portfolio is the tangency portfolio.  The market portfolio ’ s CAL is called the Capital Market Line (CML).

131.  The CML gives the risk-return combinations achieved by forming portfolios from the risk-free security and the market portfolio :

132. Step 2: What is the Risk Investors Face?  We know that for very well diversified portfolios, we can eliminate diversifiable (non-systematic) risk. But we cannot eliminate market (systematic) risk.  Under our assumptions, all investors hold very well diversified portfolios.  Thus, we assume that the relevant measure of risk for an investor is market risk. That risk is measured by beta.  Investors are only concerned with expected return and beta.

133. Step 3: What is the right Risk Measure?  Expected return increases with beta.  Treynor ’ s measure for all securities is the same: Expected return is linear in beta. (Security Market Line, SML)

134. Last Step Put j=Market

135. CAPM Result Expected (required) return on a security Compensation for time value of money Compensation for market risk = (beta) x (market risk premium)

136. Security Market Line (SML)

137. The Capital Market Line and the Security Market Line

138. Systematic and Non-Systematic Risk  The CAPM equation can be written as:

139.  This implies the total risk of a security can be partitioned into two components: bi measures security i’s contribution to the total risk of a well-diversified portfolio, namely the market portfolio. Hence, bi measures the non-diversifiable risk of the stock

140.  Investors must be compensated for holding non-diversifiable risk. This explains the CAPM equation: E(R i ) = R f +  i [ E(R M ) - R f ], i = 1, …,N

141. Example  ABC Internet stock has a volatility of 90% and a beta of 3. The market portfolio has an expected return of 14% and a volatility of 15%. The risk-free rate is 7%.  What is the equilibrium expected return on ABC stock?  What is the proportion of ABC Internet ’ s variance which is diversified away in the market portfolio?

142. Solution

143. CAPM and Expected Return The CAPM provides us with the expected return of any asset or portfolio based on its risk as measured by beta, the risk premium in the market, and the risk free rate. The difference between the asset ’ s implied expected return given by the CAPM and its actual expected return is referred to as the asset ’ s alpha. alpha - the difference in the rate of return of a security and what was predicted by an equilibrium model