Mutual Funds and Investment Companies

Mutual Funds and Other Investment Companies

• Investment companies pool funds from individual investors to invest in securities or other assets.
• They handle record keeping and administration.
• Investment companies provide diversification and divisibility.
• They offer professional management.
• Using investment companies can result in lower transaction costs.

Chapter Overview

• Topics covered include investment companies, mutual funds, unit investment trusts, hedge funds and closed-end funds.
• This sections discusses mutual fund functions, investment styles and policies, the costs of investing, performance and sources of information.

Net Asset Value (NAV)

• Investment companies pool assets of individual investors and divide claims to those assets among investors.
• NAV is calculated as (Market Value of Assets - Liabilities) / Shares Outstanding.

Investment Companies: Unit Investment Trusts

• Unit investment trusts involve pools of money invested in a fixed portfolio for the fund's life.
• They are unmanaged.
• Declined from $105 billion (1990) to $85 billion (2017).

Investment Companies: Managed Investment Companies

• Managed investment companies can be open-end or closed-end funds.
• Open-end funds redeem or issue shares at NAV and are priced at NAV.
• Closed-end funds do not redeem or issue shares, but shares are constant and priced at a premium or discount to NAV.
• Investors cash out of shares by selling to new investors.

Investment Companies: Other Investment Organizations

• Commingled funds are partnerships of investors that pool funds.
• REITs can be Equity vs mortgage trusts.
• Hedge funds pool assets from private investors. They allow private investors to pool assets to be managed by a fund manager.

Mutual Funds

• Mutual funds are open-end investment companies
• They are the dominant investment company today
• Accounts for 87% of investment company assets
• Early 2018 Assets Under Management in the U.S. - $18.7t
• Early 2018 Assets Under Management in the Non-U.S. - $25t

Mutual Funds: Investment Policies

• Money market funds invest in money market securities like commercial paper, repurchase agreements, or CDs.
• Equity funds invest primarily in stock.
• Sector funds concentrate on a specific industry or country.
• Bond funds specialize in the fixed-income sector.

Mutual Funds: Investment Policies (2 of 2)

• International funds can be global, international, regional, or focus on emerging markets.
• Balanced funds are designed as an individual's entire investment portfolio, holding equities and fixed-income securities in stable proportions.
• Asset allocation and flexible funds hold both stocks and bonds and engage in market timing.
• Index funds match the performance of a broad market index.

U.S. Mutual Funds by Investment Classification

• Largest investment type is Total Return funds with more than $5 Billion in assets

Mutual Funds: How Funds Are Sold

• Some funds are sold directly by the underwriter, the fund (i.e., direct-marketed funds)
• These are sold through the mail, various offices of the fund, over the phone, or internet
• Indirectly through brokers acting on behalf of the underwriter (i.e., sales-force distributed)
• Brokers or financial advisers receive a commission for selling shares
• Financial supermarkets sell shares in funds of many complexes
• Brokers split management fees with the mutual fund company

Costs of Investing in Mutual Funds

• Mutual funds have fee structures, including operating expenses, front-end loads, back-end loads, and 12b-1 charges.
• Fees must be disclosed in the prospectus.
• Share classes have different fee combinations.

Fees for Various Classes

• Class A shares have front-end loads and low 12b-1 fees.
• Class C shares have no front-end loads, but higher 12b-1 fees.
• Class I shares are for institutional investors and have lower fees.

Fees and Mutual Fund Returns

• Rate of return is calculated as: (NAV₁ - NAV₀ + Income and capital gain distributions) / NAV₀.
• Example with initial NAV of $20, income distributions of $0.15, capital gain distributions of $0.05, and ending NAV of $20.10.
• Rate of return = ($20.10-$20.00 + $.15 + $.05)/$20.00 = .015, or 1.5%.

Impacts of Costs on Investment Performance

• Fund A is no-load with .25% expense ratio.
• Fund B is no-load with 1.25% expense ratio.
• Fund C has a 6% load on purchases and a .8% expense ratio.
• Gross return on all funds is 10% per year before expenses.
• Investment costs can significantly impact cumulative proceeds over time.

Taxation of Mutual Fund Income

• Mutual funds have "pass-through status" - taxes are paid by the investor, not the fund.
• A disadvantage is fund investors do not control the timing of securities sales to engage in tax management.
• A high portfolio turnover rate can be "tax inefficient".
• Turnover is the fraction of the portfolio being replaced each year.
• Average turnover dropped to 30% in 2017.

Exchange Traded Funds (ETFs)

• ETFs are offshoots of mutual funds that allow investors to trade index portfolios like stocks.
• Examples include "spiders," "diamonds," "cubes".
• Trade continuously like stocks, can be sold short or purchased on margin
• Cheaper than mutual funds and are tax efficient
• Most are indexed, some leveraged
• Potential disadvantages: prices can depart from NAV and must be purchased from a broker (for a fee)

Growth of U.S. ETFs Over Time

• ETF assets include Bond, Commodities, Global/International Equity, U.S. Equity (Sector & Broad Index)
• ETF assets have grown significantly over time.

Investment Company Assets Under Management, 2018

• Assets are allocated to Mutual Funds, Exchange-Traded Funds, Closed-End Funds, Unit Investment Trusts

Mutual Fund Investment Performance

• Actively managed funds use the Wilshire 5000 index as a benchmark for equity fund managers.
• The Wilshire 5000 outperformed the average return on diversified equity funds in 29 of 48 years (1971-2018).
• 65% of active funds underperformed the S&P 500 in 2018.

Actively Managed Equity Funds versus Wilshire 5000 Index

• Charts show rates of return on both indexes and active funds compared to Wilshire 5000

Information on Mutual Funds

• The prospectus is a statement of investment objectives, describing investment objectives and policies, describing the fund's investment adviser and portfolio manager and presents fees and costs.
• SAI is the statement of additional Information.
• An additional source of info is fund annual report.

Information on Mutual Funds (2 of 2)

• There are many encyclopedias of mutual fund information available.
• Some include www.morningstar.com, www.finance.yahoo.com/funds andwww.ici.org Directory of Mutual Funds.

Risk, Return, and the Historical Record

• Chapter covering tools for estimating expected returns and risk from the historical record, interest rates and investments in safe assets and history of risk-free investments in the U.S.
• This chapter studies scenario analysis of risky investments and the data inputs necessary to conduct it, and statistical tools needed to make inferences from historical time series of portfolio returns.

Interest Rates and Inflation Rates

• Fundamental factors that determine the level of interest rates: supply of funds from savers (households), demand for funds from businesses, government's demand for funds (modified by the Federal Reserve Bank) and the expected rate of inflation.
• Interest rates are affected by supply and demand.

Real and Nominal Rates of Interest

• A nominal interest rate is the growth rate of your money
• The real interest rate is the growth rate of purchased power
• rnom = Nominal Interest Rate, real = Real Interest Rate, i = Inflation Rate
• The real rate is denoted as rreal= rnom − i / 1+i (approximately rreal ≈ rnom − i)

Determination of the Equilibrium Real Rate of Interest

• Real interest rate determined by supple and demand curve

Interest Rates and Inflation

• Higher nominal interest rates are anticipated when inflation is higher
• E(i) denotes current expectations of inflation.
• Fisher hypothesis: = + E (i)

Taxes and the Real Interest Rate

• Tax liabilities are based on nominal income, and the tax rate is determined by the investor's tax bracket.
• rnom = Nominal Interest Rate, real = Real Interest Rate, i = Inflation Rate and t = Tax Rate
• rnom(1-t)-i=(real+i)(1-t)-i=rreal (1-t)-ixt
• After-tax real return falls by the tax rate times the inflation rate.

Bills and Inflation, 1926-2018

• The Fisher equation predicts interest rates should track inflation to stabilize real rates.
• Appears to perform better when inflation is forecastable allowing investors to accurately estimate nominal interest to provide acceptable real return.

T-Bill Rates, Inflation Rates, and Real Rates, 1926-2018

• T-bills are charted alongside inflation and real T-bill rates
• Average rates and standard deviation are measured
• Source: Annual rates of return from rolling over 1-month T-bills: Kenneth French; annual inflation rates: Bureau of Labor Statistics.

Interest Rates and Inflation, 1926-2018

• Inflation charted alongside T-Bills
• Data between multiple years

Effective Annual Rate (EAR) and Annual Percentage Rate (APR)

• Effective annual rates (EAR) explicitly account for compound interest. Effective formula: (1+EAR)=(1+APR / n)^n
• Annual percentage rates (APR) are annualized using simple rather than compound interest, formula: APR = n x [(1 + EAR)1/n - 1].

Risk and Risk Premiums: Holding Period Returns

• Sources of investment risk are macroeconomic fluctuations, changing fortunes of various industries and firm-specific unexpected developments
• Holding period return (HPR), or realized rate of return, is based on price per share and cash dividends collected.
• HPR = (Ending price of a share - Beginning price + Cash dividend) / Beginning price.

Risk and Risk Premiums: Expected Return and Standard Deviation (1 of 2)

• Investors can calculate expected returns from a scenario with multiple options.
• Expected returns: E(r) = ∑p(s)×r(s), where p(s) = probability of each scenario r(s) = HPR in each scenario and s = scenario

Risk and Risk Premiums: Expected Return and Standard Deviation (2 of 2)

• Variance (VAR) is determined using squared deviation. σ² = ∑p(s)x[r(s)-E(r)]2
• Standard Deviation (STD) is the square root of variance: STD = √σ².

Risk and Risk Premiums: Excess Returns and Risk Premiums

• Risk premium is the difference between the expected HPR and the risk-free rate.
• It provides compensation for the risk of an investment.
• Risk-free rate is the rate of interest that can be earned with certainty and is commonly taken to be the rate on short-term T-bills.
• The difference between the actual rate of return and the risk-free rate is called excess return.
• Risk aversion dictates the degree to which investors are willing to commit funds to risky assets (eg stocks).

Learning from Historical Returns

• Expected returns uses an arithmetic average and treats each observation as an equally likely scenario. E(r) = Σ p(s)r(s) ==Σr(s) / n = Arithmetic average of historic rates of return
• Intuitive measure of performance over the sample period is the (fixed) annual HPR that would compound over the period to the same. Terminal value VN GA (1+g) Vn = Terminal value / V0 - 1
• GA ≈ AA - V/2

Learning from Historical Returns: Variance and Standard Deviation

• Estimated Variance; calculates a squared deviations of the means
• 𝞼² = Σns=1 [r(s)- r̄] / n _ Unbiased estimated standard deviation
• 𝞼 = Σns=1 [r(s)- r̄] / (n-1) [Where = biased estimated standard deviation and - 𝞼 = unbiased estimated standard deviation

Learning from Historical Returns: The Reward-to-Volatility (Sharpe) Ratio

• Investors value the premium of risk assets, by determining if the Sharpe’s ratio (measure of risk) meets expected excess returns.
• A higher measurement of risk by the standard deviation of excess, not total, returns will occur with a Sharpe ratio
• Sharpe Ratio is used in evaluating performance of managers _ The equation is Risk premium/SD of excess return

The Normal Distribution

• Normal distribution is a bell-shaped probability distribution that characterizes many natural phenomena
• Investment management works when returns can be well approximated by the normal distribution; its Symmetric and Stable
• Statistical relationship are summarized, by a correlation Coefficient

The Normal Distribution part 2

• Symmetric, and Stable
• relation summarized with correlation coefficient

Deviations from Normality and Tail Risk

• Skewness- standard measurement of asymmetry
  • STD no longer measure risk (performance) Skew = Average(R – R)3/2 / 𝞼3
• Kurtosis- concerns the likelihood of extreme values
  • measures the degree of fat tails Kurtosis = Average(R – R)4/2 / 𝞼4

Skewness and Kurtosis

• Normal and Skewed Distribution, Normal and Fat tailed distributions chart

Normality and Risk Measures: Downside Risk

• Value being measure when dealing with Normal values and downside risk
• Loss to be expected from extremer price changes Value at risk (VaR)
• measure risk by the rate of distribution & Deviation Standard (LPSD)
• relative negative Large Frequency

Historic Returns on Risky Portfolio

• Measure using Stocks T-bonds and T bills
• Premium, standard of deviation for the Max, Min to analyze the risk

Historic Returns on Risky Portfolios:

• A Global View of the Historical Record
• Century plus Long history 1900-2017 in 20 Stock Market.
• 7.4% returns and 6.6% median
• Variance shown in year by year in return.
• US performance is consistent with International returns.

Average Excess Returns in 20 Countries, 1900 - 2017

• Risk Premium (%) 0 6 12 10

Normality and Long-Term Investments

• Lognormal distribution- probability distribution that is well shaped
• Has a normal distribution(Bell shaped)
• uses continuously compounded returns, instead of annual returns.
• Short-run for returns versus Long run

Capital Allocation to Risky Assets

• A portfolio construction that's uses a Two-step process

1. Capital allocation decision to safe asset vs risky asset
2. determination of composition of the risky assets vs the portfolio

• How a risk-aversion can be by “utility function” for characiterized for demonstration

Risk and Risk Aversion:

• is risk - using the proper perspective
• Speculation- investment that is consider a gain and risk taken but a favorable return
• Gambling-risk assumed for the enjoyment, which may present itself

Risk and Risk Aversion:Utility Values

• High, and postive risk premiums can be present with speculative projects
• Return is high and risk is low
• What increase when the what if risk is there within return

Available Risky Portfolio

• Table listing low, medium, and high risk in portfolios.

Risk and Risk Aversion (Utility Values Continued)

• Welfare and utility values, can assume any investor U= E(r)- 1/2 A𝜎2 utility function
• where U= Utility values,E= expected returns, and A index investors to aversion risk, and 𝜎 variance returns

Example

• Lists out what Utility score of alternative investor has or doesn't based on certain degrees of ris aversion

Investor Types

• Types are only considered of composition with the certain compensation via premium, because their risk-avert -High, low
• Irrelevant to prospect of consider, risk neutral
• Accept for less amounts of risk by consider prospects lover
• amount of prospect

Trade-Off Between Risk and Return

• This trade-off refers to maximizing the different rates of returns

Mean-Variance (M-V) Criterion

• The minimum variances is with selection ,as well a • portfolios
• • as well as a, selection for the higher variances
• Requirement portfolios are to dominance it as well.
  • Inequality is one strict by being all for portfolios

Indifference Curves

• the standard deviation mean that equally preferred, lies on indifference curve, connects which values are utility all

Estimating Risk Aversion

• Estimating to what is asked for questionnaires with different degrees of complexity
• How its composed over time
• And degree is average by the individuals

Capital Allocation Across Risky and Risk-Free Portfolio

• Control risks by asset allocation for different classes
• Allocates to both risk and safe for best

Basic Asset Allocation Example

• Example of allocation and division calculations to asset allocation

The Risk-Free Asset

• Government backed security as default
• Guarantees real returns with indexed price
• Short Term T Bills and market tools

Portfolio is with

-splitting of investment for safe and risky balance with a range -Portion allocated to risky(p) And in a T Bill(F) is at (Y-1)

Risky as Risk-Free Asset

An examples is at a 10% Premium with complete profile

One Risky Asset and a Risk-Free Asset example

• 2x = Standard Divination/ and with allocations of investment for what their weight is.

The Investment Opportunity Set

• The Efficient to the right CAL Asset

One Risky Asset and a Risk-Free Asset Portfolio

• Risk is with both Standard Division to meet allocations with
  • Ratio & and the Sharpe Ratio-

Risk Tolerance and Asset Allocation

• Find the right opportunity at a stable level
• Find portfolio using these Expected/ Yx [Exp-s] And Variance-

Utility Levels for Various Positions in Risky Assets

• Chart that determines where best position is from the rate to risk of account's asset

is a function of allocation,

• graph to make it very easy where asset allocation is the best for it

Utility as a Function of Allocation to the Risky Asset

• Maximizing which is with
  • (R (41 = Re + (x(P)-r] / (2x2

Calculations of Indifference Curves

• Charts shows at all the rates, the indifference is great

Indifference Curves for with A

• At four different points what indifference there is and how equal
• what is better is with a graph

Finding the Optimal Complete Portfolio

• Portfolio made using
  • CAL with standard -and that all meets in the middle

Expected Returns of Four Indifference and the CAL

• Return to the CAL and indifference with expected rates

Non-Normal Returns

• Implicit assumes as Analysis and deviation and appropriate measures -Value of ES is used to access the Value loss
• Back swan events are concerned by investors

Passive Strategies

• Capital markets to be best, may make that strategy be choice with the best for many investors and its low cost
• Canidat that's held and verified can use capital and portfolio (s and p portfolio)