Posted: September 13th, 2017

Optimal Portfolio Project

Paper, Order, or Assignment Requirements

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.

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:

edu/~stambaug/portopt.html”>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 (R_portfolio )  – .5γσ²