## Archive for May, 2008

### Modern Portfolio Theory Part V: The Sharpe Ratio

Wednesday, May 7th, 2008

In the April 21-24 blogs, one of my guest contributors, Professor Pat, tackled the esoteric subject of Modern Portfolio Theory (MPT). Using data from 1927 to the present, he derived an asset allocation table that an investor can use to construct his or her own optimally allocated investment portfolio according to an investor’s requirements for portfolio return versus risk. Today, he’s extending his presentation to include the Sharpe Ratio and how that can be used to further increase portfolio returns while simultaneously minimizing risk. Take it away, Professor!

This installment in the Modern Portfolio Theory (MPT) series will discuss the concept of the efficient frontier, the Sharpe ratio as applied to MPT and how to add a riskless cash component to your portfolio. The discussion is applicable to interest rates and optimum portfolio allocations and returns current to today.

The Efficient Frontier
In Part III of this series (see April 23 blog) a table was presented entitled ”Optimum Asset Allocation Among Investment Classes” whose first two columns were Required Return and Standard Deviation. Let’s now plot those two columns (and many more data points in between) on the graph shown below. The resulting magenta line is known as the “efficient frontier” as is represents those optimally efficient portfolios that provide the least amount of risk for each level of return in today’s market. The shaded area underneath the curve represents the possible space of less efficient allocations of portfolio assets.

Note that the efficient frontier is a curved convex line. This is a result of the lack of correlation (see Part IV, April 24 blog) between the various assets in the portfolio and how that results in an optimum portfolio characterized by an overall standard deviation less than it would be for one of completely correlated assets. Remember, for uncorrelated assets when some are up in value others are down in value and the overall portfolio therefore exhibits reduced variation. For a portfolio of totally correlated assets a combined linearly weighted standard deviation would result and the efficient frontier curve would be straight rather than curved. It is the existence of optimum allocations that pulls the line to the left for a lower standard deviation at each point that creates that convex shaped curve. The end points of the curve do not benefit from this left pulling because they are dominated by portfolios containing a high percentage of a single asset class–at the high end of the curve, the optimum portfolio is composed of 100% in Small Stocks and at the low end by 93% in Treasuries. The convexity of the efficient frontier curve therefore graphically demonstrates the beneficial effects of diversification.

Adding a Cash Component and The Sharpe Ratio
The Sharpe Ratio, S, is named after William Sharpe, who won the 1990 Nobel Prize for his work on the Capital Asset Pricing Model which shows how the market prices individual securities in relation to their asset class. Here the discussion is limited to the Sharpe Ratio which, for a particular investment, is a direct quantitative measure of reward to risk. It is a measure of how much excess return a portfolio provides above a riskless investment considering the additional risk it entails. It is defined as:

S = (Portfolio Average Rate of Return – Current Rate of Return of a Riskless Investment) / Standard Deviation

Let’s look at the line of best capital allocation on the graph above. This line represents the best way to incorporate a riskless cash component into an already optimum portfolio thereby reducing the risk even further albeit at a reduced overall rate of return. As of this writing, the annual rate of return on a 30-day United States Treasury Bill is about 1.2%. This is considered the safest investment for the short term and is considered to be as riskless as cash. The line on the graph therefore starts at 1.2% plotted at zero standard deviation (it’s riskless!) and is drawn so that it contacts the efficient frontier curve at a point such that the slope of the line is a maximum. This is the point on the efficient frontier with the greatest Sharpe Ratio and is known as the market portfolio. The slope of the line is the Sharpe Ratio for the market portfolio and the current riskless rate of return. As seen on the plot above, the market portfolio provides about a 5.0% return which has a standard deviation of 3.4%. You can confirm this in the table from Part III. The Sharpe Ratio for this investment is therefore (5.0 – 1.2) / 3.4 = 1.12 which, as we have noted, is also the slope of the line of best capital allocation.

Note that the black line is straight because the riskless investment has no standard deviation and there is no better “optimum” allocation that will produce a resultant combined reduced standard deviation that would produce a convex curve like that for the optimum allocations of the other investment classes.

Investments anywhere on the line of best capital allocation give you the overall return and standard deviation of an optimally allocated investment combined with an additional riskless cash component (the optimum allocation for the 5.0% return already has about a 70% 30-day T-bill component which in the long term has a nonzero standard deviation but that is immaterial for this analysis of the current state of interest rates and the market). In this way you can easily construct a composite portfolio that is also optimum but that has a reduced standard deviation resulting from adding a riskless cash component. This is of course at the penalty of a lower overall portfolio return. The percentage of cash to include in the composite portfolio is easy to determine since the standard deviation is reduced linearly according to the slope of the line (the Sharpe Ratio). For example, a portfolio of assets at risk returning 5.0% with a standard deviation of 3.4% can be reduced to one with a standard deviation of 2%. From the graph, such a portfolio returns about 3.2% and is constructed by reducing the component of optimally allocated risky assets to 64% (3.2 / 5.0) x 100% and by adding a 36% (the rest) cash component.

Increasing Potential Returns Through Margin Borrowing
Instead of adding a cash component to your portfolio you can choose to borrow against the market portfolio and realize increased potential returns. Naturally, doing this also increases risk.Whereas a portfolio with an added cash component and lower risk resides on the line of best capital allocation at or below the market portfolio, a portfolio that has been borrowed against will reside on the line of best capital allocation above the market portfolio. A higher risk, but still optimum, portfolio can be formed by borrowing against the market portfolio on margin (assume the rate of borrowing is also at the riskless rate of interest). You then reinvest the borrowed cash right back in the market portfolio in the same proportion as assets that portfolio already holds. So now you have a portfolio allocated exactly the same as the market portfolio but it now has a higher value. But you have margin debt to pay at a lower rate than the portfolio is expected to produce on average. The standard deviation of returns this portfolio will exhibit is greater than the market portfolio as seen as you climb up the line of best capital allocation. Hopefully the result will be positive. This expanded portfolio residing on the line of best capital allocation which has a slope equal to the Sharpe Ratio exists in a region above the market portfolio contact point on the efficient frontier. It is there on that line that you can decide the standard deviation and thus the amount of additional risk you’ll have to take in order to achieve a higher return.

Dr. Kris Note: I know that these discussions on MPT might be flying over the heads of many of you, but it is something that every serious investor who does his own portfolio asset allocation should try to understand because these tools can be used to effectively increase returns while minimizing risk. I think that’s a good enough reason to merit these discussions.

### Better Than A Money Market

Tuesday, May 6th, 2008

In today’s turbulent market environment, many risk-adverse investors have wisely moved into cash, parking their money in money market accounts. Currently, money markets are paying two to three percent on average, but might there not be other investment vehicles that pay more while still being low-risk? The answer, of course, is yes. (If the answer was no I wouldn’t have an article.)

So, what are these investment vehicles? They’re are old friends, the exchange-traded funds (ETFs). If you don’t know what an ETF is, it’s a mutual fund that trades on the American stock exchange (AMEX) just like a stock. That means that you can buy them at any time during market hours unlike a mutual fund which only trades at the end of the day. ETFs are linked to an index which means that they are passively managed (although the underlying index might not be) which keeps expense ratios low, much lower than their mutual fund counterparts.

The past several years has seen an explosion in the ETF universe. If there’s an index out there, there’s probably an ETF that tracks it. The largest fund issuers are PowerShares, Vanguard, State Street Global Advisors, and Barclays. For income investors as well as the gun-shy investor, here’s a list of ETFs that are relatively risk-free and pay higher returns than a money market. The good news, too, is that some of them are completely tax-free or are taxed at lower rates.

1. State Street’s Lehman Muni-Bond (TFI): Tracks the Lehman Brothers municipal bond index.
Current NAV (net asset value): \$22
Current Yield: 4.52%
Tax-equivalent Yield: 6.05%
Expense Ratio: 0.2%

2. PowerShares Insured California Muni-Bond (PWZ): Based on the Merrill Lynch California Insured Long-Term Core Municipal Securities Index, which is designed to track the performance of AAA-rated, insured, tax-exempt, long-term debt publicly issued by California or Puerto Rico or their political subdivisions. (Puerto Rico is tax-free for all states.)
Current NAV: \$24
Current Yield: 4.21%
Expense Ratio: 0.28%

3. PowerShares Insured New York Municipal Bond (PZT): Based on the Merrill Lynch New York Insured Long-Term Core Municipal Securities Index, which is designed to track the performance of AAA-rated, insured, tax-exempt, long-term debt publicly issued by New York or Puerto Rico or their political subdivisions.
Current NAV: \$24
Current Yield: 4.17%
Expense Ratio: 0.28%

4. PowerShares Insured National Municipal Bond Portfolio (PZA): Based on the Merrill Lynch National Insured Long-Term Core Municipal Securities Index, which is designed to track the performance of AAA-rated, insured, taxexempt, long-term debt publicly issued by U.S. states or their political subdivisions. This fund can be considered safer than the TFI since all of the bonds here must be insured compared with only 46% in the other.)
Current NAV: \$24
Current Yield: 4.19%
Expense Ratio: 0.28%

5. PowerShares Emerging Markets Sovereign Debt (PCY): Based on the Deutsche Bank Emerging Market U.S. Dollar Balanced Liquid Index, an innovative index developed by Deutsche Bank Securities Inc. that provides intelligent access to the sovereign debt of approximately 17 emerging market countries. Although you may think this portfolio is high-risk, it’s not because it invests in sovereign debt as opposed to corporate debt making it much lower risk.
Current NAV: \$26
Current Yield: 5.59%
Net Expense Ratio: 0.50% (This is the highest expense ratio of the bunch, but note that it’s the same as the Lehman International Treasury Bond ETF.)

This is a sampling of some of the ETFs that you can substitute for a money market. Although you don’t have some of the conveniences that a money market offers, like writing checks for example, you do have the ability to liquidate your positions easily if you do need some cash.* And compared with mutual funds that can require several thousand dollars to buy their product, there’s no required minimum investment.

So when’s the best time to buy these products? Well, when the net asset value (NAV) is low. Duh. All of these ETFs hit their historic lows on February 29th and have been recovering since then. If any of these products interest you, now would be a good time to buy. Although it may seem counterintuitive, the Emerging Markets ETF, the PCY, has been the least volatile of the bunch, trading in a very tight range between \$25 and \$26. It also adds a bit of diversity to the above products as the international market is less tied to the US market (less correlation).

Now you don’t have any excuse to keep all of your cash tied up in a low-paying money market!

*A note on trading liquidity: Some ETFs, notably the PWZ and the PZT, have low trading volumes (<10,000 shares per day) but please don't confuse low volume with liquidity. ETFs are open-ended investments as compared with closed-end funds. A closed-end fund can suffer dramatic changes in their NAVs if there is a spike in trading volume, but not ETFs since new shares can always be created. This maintains the stability of the NAV which in essence should reflect the value of the portfolio's holdings. Moral of the story: Don't be afraid to buy into an ETF that trades on low volume.

### Ya-Boo!

Monday, May 5th, 2008

As I’m sure you already know, internet giant Yahoo! this weekend rejected Microsoft’s take-over offer after they upped their bid by two bucks to \$33/share. The suits in charge at Yahoo! felt that their company was worth at least \$4/share more and felt slighted by the paltry increase. Of course the question on everyone’s minds is not if Microsoft will still pursue the merger but if any sort of merger will be happening with either of the companies. Both sides of this question are currently being bandied about in the financial media and I’m not going to regurgitate the arguments here.

What I do want to focus on is if there’s a possible play in all of this. In my blog on February 1st when the proposed merger was first announced, I suggested buying Yahoo stock at the going price of around \$28/share and writing the April 30 covered call (trading then in the \$1.50-\$1.60 range) against it. That call would have expired worthless on Friday, April 18th and if you had again written the May 30 call in the \$0.80 – \$1.00 range on the following Monday, you would have at least cushioned yourself against today’s 15% drop in Yahoo! share price. Had you written these calls, your cost basis would have been lowered to around \$25.50 thus limiting today’s loss to about 5% instead of 15%. This is one good reason to use covered calls on controversial take-over targets.

This play is a no-brainer in retrospect as hindsight is always 20/20. But is there still a way to profit from this situation? It’s anyone’s guess but the word on the street is that some sort of merger is probably in the offing since they’re highly skeptical that Yahoo! will be able to live up to its financial targets. Perhaps in the short term this could put downward pressure on Yahoo! shares, but if the price falls too far, the board can surely expect a bunch of shareholder lawsuits (some are already suing the company). Whether or not Microsoft steps back into the picture is immaterial; what really matters is that someone will and probably sooner rather than later.

If I believe this (and I do), here’s how I would play it. If I’m still short the May 30 calls, I’d buy them back today for ten cents. I’d wait a day or two and if the stock doesn’t tank, I’d either write the July 25 calls or buy them outright. (These calls are trading today for around \$2/contract.) In the event that a merger is announced between now and the middle of July, the share price will go up and at worst my stock will be called away at \$25/share. Since my current cost basis is \$25.50/share means that I’ll have pocketed an extra \$1.50/share which translates into a 5-6% return. If I buy the calls instead of selling them will give me a much larger return. Even if Yahoo! accepts a price that is close to Microsoft’s original bid of \$31/share means that at on or before expiration, my calls will be worth at least \$6/contract giving me a minimum 200% return on my investment. ((\$6 final price – \$2 cost)/\$2 cost basis x 100%). I like that type of return. The only possible wrench in the gears is that Yahoo!s share price falls substantially but I really don’t think that the Yahoo! shareholders are going to let that happen.

Actually, Mister Softee might have done us a favor by letting us turn a Ya-Boo! into a Ya-Hooooo!!!!

### Tech Talk: A Portfolio of Technology Stocks

Friday, May 2nd, 2008

Well, it appears that the Fed didn’t disappoint and either did today’s jobs report. The news cheered up a gloomy Wall Street as evidenced by recent market action. With the S&P breaking through its all important 1400 ceiling yesterday combined with the VIX (volatility index) hanging below 20, it appears that we have the making of the next bull market. As always, the perennial question is: What to buy?

A guest commentator on CNBC yesterday said that institutions are returning to the market and are rotating some of their positions out of sectors that have been performing well, such as materials and commodities, and pumping money into technology stocks. Although disappointing earnings from Sun Microsystems stalled the tech rally today, I still think the entire sector has been oversold and is poised for a turnaround. (Many of the tech ETFs were down 25%-40% from just a year ago.) If you look at their charts, you can see that they’ve all been rising steadily since the middle of January when the overall market hit its nadir. Rather than buying these ETFs outright, I thought it might be fun to cherry pick the best of each and construct our own portfolio.

Portfolio Construction
What I did was to look at the charts of the top ten holdings of each of the following ETFs and then select the top one or two stocks whose charts I found to be the most compelling:

IAH & XLK – Internet Architecture/Technology: Cisco (CSCO) & Network Appliances (NTAP)
SMH – Semiconductors: Intel (INTC) & Xilinx (XLNX)
TTH – Telecom: AT&T (T) & Verizon (VZ)
BDH – Broadband: Research in Motion (RIMM)
IIH – Internet Infrastructure: RealNetworks (RNWK)