Optimal Portfolio project
Use Excel, Yahoo-Finance, and a portfolio optimizer available on the web. If you have a statistics package like E-views, Stata, SPSS, SAS, Statistica, RATS, Shazam, TSP, PC-Give, or something else you can use that package.
In addition, do research on what type of alternative investments to consider for inclusion in your optimal portfolio. Look into alternatives for investors to get above the risk-free rate in an environment of stable or rising interest rates. Consider both a conservative and an aggressive investor.
(1) You are advising a client about how to historically create the optimal portfolio and which asset classes to include. For example, do you include real estate? How? Do you include commodities? How? Which ones? (The easiest is to use REITs, and various exchange traded funds for as many asset classes as possible. You must find a stock fund, a bond fund, a real estate fund or a REIT, and something with other alternative asset investments. You will discuss the various asset classes you have considered for the optimal portfolio. There are various alternative asset ETFs and hedged ETFs to consider. Also examine international stocks and bonds, hedge funds, and private equity.
(2) You are also expected to give advice on how to construct a portfolio if the future is not quite like the past. How can you still earn reasonably high returns in an environment of diminished earnings expectations for stocks and bonds ( a feeling that we may be in a period low returns for stocks and bonds, a future where we likely have rising interest rates, and where people are still likely risk-averse, but want more than the extremely low return on T-bills or money market funds (for example how do you get more than 0.1% to 0.7%? without taking on excessive risk?)
You are going to go to Yahoo-Finance to get returns. You can do these monthly. Ideally you will find at least 10 years of returns.
If this is not possible, do 5 years of returns (you will need 61 months of prices to get 5 years of returns).
Some examples of funds on Yahoo include: AGG, SPY, GLD, SLV, CORN, FXI, EWU, DBC, but also find some Canadian funds.
Use your return series and obtain historical values for returns, standard deviations, and correlations for lots of asset classes.
Then plug various combinations of these numbers into the Efficient Frontier optimizer program.
Go to this site to calculate efficient frontiers:
http://finance.wharton.upenn.edu/~stambaug/portopt.html
Pick a degree of risk aversion for yourself (you decide). Then choose a different degree and look at how the optimal portfolio changes.
1. Find an optimal portfolio for 2 assets (agg and spy) for US, or do the same for Canadian bonds and stocks
Initially do not allow short sales.
Interpret results. (That is: What is the return and standard deviation? What are your percentage weights for bond versus stocks?)
How does investing in US and Canada compare historically?
2. Now select a 4 asset portfolio (you pick the assets). Interpret your results.
Show the return and standard deviation.
What are the weights for the 4 asset classes?
Compare it to the return and standard deviation of the optimal 2 asset portfolio. Are there benefits from holding 4 assets versus 2? (THERE SHOULD BE)
3. Do the same as in question 2, but now move up to 8 assets. Find the optimal weights. Show the benefits of moving up to 6 to 8 asset classes. You may end up with less than 8 assets if some have lower returns or higher risk, but indicate which assets you dropped.
4. Discuss possible problems with choices of asset classes. You may have to delete some and add others even if it means getting lower returns. This is due to problems encountered in many optimizer situations. Present your final portfolio and recommendations in general for inclusion of asset classes.
5. Finally, discuss alternatives in the possible difficult future situation where the past may not be repeating itself for several years. Indicate what you recommend. Tell and sell your story. This may involve several pages of writing and you can quote other people here. List references for this part.
This will be a group project and may end up being 10-12 pages including computer output.
For those of you wishing to present in front of the class, all I ask you to do is the 2-asset class portion of this assignment.
Comments on CRRA Utility functions: U = E (Rportfolio ) – .5γσ2
This is a constant relative risk aversion utility function, where the coefficient (γ ) or gamma, reflects the investor’s degree of risk aversion. A value of gamma = 0 would be a risk-neutral investor.
A value of gamma = -1 would be a risk seeking individual.
For the online optimizer, you cannot input zero or negative risk aversion coefficients.
I think it accepts anything from about 0.1 and higher, but you get strange results for any number below about 0.6. A value of γ=1 is considered to be a very aggressive investor.
Azar (2010) in Banking and Finance Letters has estimated gamma values for individual investors and for mutual funds. The range seems to be form γ = -1 for certain risk seekers or gamblers up to about γ = 7 for very conservative investors.
Values above 7 for gamma really imply that such an individual should not even be considering stock market investments.
The so called “typical investor” and hence a typical mutual fund would have a rage of values of gamma from γ = 3.0 to γ = 3.5. Use that as your base and decide where you fit in. If you are giving advice in general, this is a good number to use—either 3 or 3.5.
Also, notice that σ2 represents variance or standard deviation squared for a portfolio or a single asset. Notice the negative sign in front of the 0.5 and the coefficient of risk aversion. It reflects the idea that variance, standard deviation, and volatility are bad for investors.
To use the optimizer, you will need a return series for each asset.
These can be either arithmetic mean returns, or approximate compound mean returns, or geometric mean returns. You just have to use the same type of mean for all assets considered. You can use either monthly returns or annualized returns from the monthly returns series.
Again, just be consistent and you have to use the same format for standard deviation. In the optimizer, you enter mean returns in decimal format.
You also enter standard deviation in decimal format.
The other input you will need is a correlation matrix between all assets being considered. You can calculate all of these inputs using an excel spreadsheet.
First download price data from Yahoo. Get as many months as you can, but realize that the length may be constrained by your shortest time series of prices.
So, try for 10 years, or 121 months of prices, but you may have to settle for 61 or perhaps 73 months of price data. Then you convert each price series into returns. You can put returns these in columns and find means, standard deviations, and get correlations using standard excel math and stat functions.
You are being asked to find the optimal allocation for two assets: stocks and bonds.
Do it for US and for Canada and present asset allocation results. Also look at what happens if short sales are allowed.
Then go to multiple assets. Your optimal portfolio should have at least 6 asset classes and may have up to 8. You report on optimal or final weights for various assets.
If a particular asset class gets a Weight above75% in your optimal portfolio, it says there have been some unusual positive or negative returns and that this asset class recent performance is not indicative of a longer history for this asset class.
You will need to constrain or put a bound on this asset class, or perhaps not include it because of unusual recent data. Actually any allocation for a particular asset class above 50% will be unusual.
Your group project will be write up you results and make comments and recommendations about asset allocation and the optimal portfolio. You can use any standard format. The second half of your typewritten report should examine alternative asset classes and make recommendations about what an investor should do for the future given potentially low bond returns, volatile stock returns and problems with potential inclusion of commodities and other asset classes. There is no right or wrong answer for this part, you are judged by the type of research you do and how persuasive are the arguments you make. You should try to find outside sources that corroborate some of your recommendations.
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