Accelerate Return-to-Risk Ratios with Higher Betas

By Chuck LeBeau,  Director of Analytics, SmartStops.net    (originally published in April 2009)

Modern portfolio theory is based on the premise that volatility is the best definition of risk. However, like many popular assumptions, that may not be entirely true. The equity markets of 2008 and 2009 took a rollercoaster ride and were overshadowed with unprecedented volatility which forced many to re-evaluate the industry and assess the changes that have come forth over the past years.

Although the basic fundamentals and principles of investing have remained the same, and successful investors continue to be the ones who can balance the risk and reward trade-off, it is now apparent that investors can’t control the reward side and that controlling the risk side is the key to preserving equity. In fact, a survey conducted by Charles Schwab indicated that 45% of investors would choose an advisor who provides products which protect them against market risks over one that doesn’t.  This article will demonstrate how increased volatility, as measured by Beta, can be harnessed to provide higher returns without a commensurate increase in risk   Assume that an investor has the choice of risking 1% of the value of his portfolio in a low Beta stock or risking 1% in a high Beta stock. Obviously if the risk is 1% in both situations the investor’s choice should be governed by the potential reward. Although both of these investments will have the same risk the higher Beta stock is more likely to provide the higher return. However, as always, there is no free lunch. In order to make
the risk of both investments equal the investor must take a larger position in the low Beta stock and a much smaller position in the high Beta stock.

Here is an example of how that position sizing process might work: Assume there are two accounts and both have $500,000 in cash to invest. The first step is to invest this money while limiting the risk of each new investment to no more than 1% or $5,000. Risk will be limited by using a strategy of placing exits below the purchase price and then adjusting the amount of stock we purchase to match the risk of that particular exit placement. Using an exit that is only 1% below the purchase price would be simple but that exit would be much too close. We must first identify a logical exit point that takes each stock’s volatility into account so the exit is unlikely to be triggered by the random up and down price gyrations that are normal for that stock. When volatility is considered in the placement of the exit, low Beta stocks that have low volatility will have exits that are close to the entry price. In the meantime, the high Beta stocks will have wider exits that allow for the bigger price swings that define these volatile stocks.
Note: It is very important that the exits used adapt to the volatility of the stock they protect. These exits are calculated at www.SmartStops.net . These are the exits that will be used in this example.

We did not want to skew the results by hand picking the stocks used in this exercise. To avoid any bias created by the stock picking methodology, we ran a simple stock scan using Google Finance that ranked stocks by capitalization and also reported their current Beta. Then we started with the largest capitalization stocks and worked our way down the list extracting those stocks with the highest and lowest Betas. The low Beta stocks had to have a Beta below 0.75 and the high Beta stocks needed to be above 1.50. Here is the list that resulted from this simple screen: Large Cap Stocks with Lowest Betas:
WalMart Stores (WMT) – Beta 0.22
Exxon Mobile (XON) – Beta 0.49
Johnson & Johnson (JNJ) – Beta 0.55
Proctor and Gamble (PRG) – Beta 0.59
AT&T Inc. (T) – Beta 0.67
Large Cap Stocks with Highest Betas:
Barclays PLC (BCS) – Beta 2.78
Bank of America (BA) – Beta 2.41
Banco Bradesco (BBD) – Beta 1.94
Banco Santander (STD) – Beta 1.94
Vale SA (VALE) – Beta 1.74
Petro China Ltd. (PTR) – Beta 1.71
China Petroleum and Chemical (SNP) – Beta 1.69
Apple Inc. (AAPL) – Beta 1.64
Siemens AG (SI) – Beta 1.61
Rio Tinto PLC (RTP) – Beta 1.55
Petroleo Brasiliero (PBR) – Beta 1.54

Notice that the list of high Beta stocks is much longer than the list of low Beta stocks. As will be seen in a minute, we will need more stocks in our high Beta list because our positions in the high Beta stocks will have to be very small in order to limit the risk to only 1%. Therefore we are going to need a much longer list to fully invest our $500,000 using high Beta stocks with their wide exits and small position sizes.
Since all we need is a very short and simple test to demonstrate our point, we are going to buy each of the stocks on April 1st and exit on July 31st of 2009. We will be looking at results after only four months of data in a rising market environment.

Here is the explanation of how we will decide how many shares to buy:

Let’s start with WalMart Stores, the first stock on our low Beta list. We are buying WMT at $50.05 per share and using the volatility adjusted exits from SmartStops we know that our loss should be limited by an exit at $47.73. With that exit point we can expect that we might lose $2.32 per share if our exit gets hit. If we divide our 1% risk ($5,000) by $2.32 we find that we can buy 2155 shares of WMT while limiting our risk to only 1% of our $500,000 portfolio. If we do that same position sizing calculation for each of the stocks on our list the fully invested low Beta portfolio would look like this:

Low Beta Portfolio – $500,000 with 1% risk limit per stock

Stock Entry price Stop-loss exit  Risk per/share   # shares bought   Amount
WMT           $50.05       $47.73          $2.32           2155          $107, 866
XOM            $68.01       $64.08           $3.93          1272              $86,527
JNJ              $52.59       $50.59           $2.00          2500           $131,475
PG                $49.50       $46.84           $2.66          1880              $93,045
T                   $26.01       $24.72           $1.29          3000             $78,030

Avg. $2.44      Total $496,943

Note: to avoid investing more than our total of $500,000 we had to slightly reduce the number of shares of our final AT&T purchase. (With risk of $1.29 per share we might have purchased 3,875 shares if we had enough money. As we will see, this 875 share adjustment reduces the final results by less than $200.)

Now let’s look at the construction of the high Beta portfolio. Note the larger risk per share due to the higher volatility and wider exits. However, higher risk per share simply tells us that we must buy fewer shares to keep our risk under control.

High Beta Portfolio - $500,000 with 1% risk limit per stock
Stock    Entry price    Stop-loss exit    Risk per/share   # Shares purchased   Amount
BCS            $16.31         $12.88             $3.43          1458             $23,776
BAC           $8.70           $7.81              $0.89          5618              $48,876
BBD           $12.62        $10.53             $2.09          2392              $30,191
STD            $9.25           $7.72              $1.53          3268              $30,229
VALE       $17.42        $15.00             $2.42         2066               $35,992
PTR           $88.95       $83.67             $5.28            947               $84,233
SNP          $78.72        $73.13             $5.59            894               $70,411
AAPL     $127.24      $116.27         $10.97           456               $57,995
SI              $67.75        $58.62             $9.13             548                $37,103
RTP        $172.01     $140.68           $31.33             160                $27,451
PBR          $35.02       $30.56              $4.46            1121               $39,260
Avg. $7.01       Total $485,517

Now let’s analyze the results and see how these two portfolios performed. Our brief study was in a rising period of the market so we would expect both portfolios to be profitable.  They were.   But the low Beta portfolio made only $35,369 while the high Beta portfolio made $135,671.  Here are the details:


Low Beta Performance

SYMBOL    May 1-ENTRY    July 31-EXIT   Gain per Share  # of shares  Total Gain(Loss)
WMT           $50.05                 $49.88             -$0.17            2155             ($366)
XOM            $68.01                 $70.39               $2.38            1272             $3,028
JNJ              $52.59                 $60.89               $8.30            2500          $20,750
PG               $49.50               $55.51                $6.01            1880           $11,297
T                  $26.01               $26.23                $0.22           3000               $660
Total profit: $35,369

High Beta Performance
Symbol    May 1 -Entry July 31-Exit  Gain per Share  # of shares  Total Gain(Loss)
BCS              $16.31         $20.54             $4.23            1458                 $6166
BAC             $8.70            $14.79            $6.09           5618              $34,213
BBD            $12.62            $15.77           $3.15            2392                $7,536
STD              $9.25            $14.46            $5.21            3268              $17,026
VALE        $17.42           $19.73            $2.31            2066                $4,773
PTR           $88.95          $117.75        $28.80              947              $27,273
SNP           $78.72           $89.36         $10.64              894                  $9,517
AAPL      $127.24        $163.39          $36.15              456              $16,477
SI               $67.75          $79.48           $11.73             548                 $6,424
RTP         $172.01        $167.58           -$4.43              160                  -$707
PBR           $35.02           $41.24             $6.22             1121                 $6,973
Total profit: $135,671

As we would have expected, in a rising market the high Beta portfolio performed best so no surprises there. But what would have happened if the market was weak instead of strong and we were stopped out of all of our positions. In our worst case scenario our prudent position sizing based on the predetermined exit points limited the loss on each position to a maximum of $5,000. So the loss on each position was the same whether it was high Beta or low Beta. But since we had eleven positions in the high Beta portfolio and only five positions in the low Beta portfolio, the high Beta portfolio would have lost more in total. At $5,000 per loss, the low Beta portfolio would have lost $25,000 while the high Beta portfolio would have lost $55,000.

So far we have only demonstrated that in a rising market a high Beta portfolio will be more profitable than a low Beta portfolio. We have also concluded that in a down market a fully invested high Beta portfolio will do worse than a fully invested low Beta portfolio.  Nothing new and   exciting has been demonstrated so far; but let’s look closely at the return to risk ratios of these two portfolios. The low Beta portfolio risked $25,000 to make a return of $35,369. That is a return to risk ratio of 1.415. That’s a respectable return thanks to the rising market in our study period.  But the high Beta portfolio risked $55,000 for a return of $135,671. That’s a much higher return to risk ratio of 2.467. We have very clearly gained Alpha by increasing Beta.

Here is another way we might look at these results: In the low Beta portfolio our average position size was $99,389 and our average profit was $7,074. In the high Beta portfolio our average position was much smaller, only $44,138, while our average profit was much larger at $12,334. In the low Beta portfolio for every $5,000 of risk we earned a return of $7,074. In the high Beta portfolio for every $5,000 of risk we received a much higher return of $12,334.  We previously pointed out that the high Beta portfolio had higher total risk.  Let’s look at that risk again.  The higher risk was entirely due to the fact that we choose to have more positions in the high Beta portfolio in order to be fully invested. But what if we chose not to be fully invested in high Beta stocks and simply had five high Beta positions to match the number of positions in the low Beta portfolio?

To avoid picking and choosing five specific high Beta stocks let’s just use the average numbers. The average position size of the high Beta purchases was $44,138 and the average return was $12,334. If we multiply those averages by five, using the assumption that we only initiated five high Beta positions, then the total risk of both the fully invested low Beta portfolio and the partially invested high Beta portfolio would be
identical. Both portfolios would be risking a total of $25,000 ($5,000 on each of five stocks). The low Beta portfolio still has five large positions with a total of $496,943 invested. In the meantime the high Beta portfolio, with only five smaller positions, has only $220,690 invested. However, with less than half of the available funds invested the high Beta portfolio still produces a higher return (5 x $12,334 = $61,670) than the fully invested low Beta portfolio (5 x $7,074 = $35,370). The high Beta portfolio returns 74% more than the low Beta portfolio without a penny of increased risk. It should also be noted that the high Beta portfolio still has $279,310 that was never invested. What might
we have done with those funds to further increase our returns? My suggestion is that by limiting risk using volatility based protective stops and then accurately sizing the position to limit the risk to a fixed percentage of capital, returns and return to risk ratios can be increased by adding higher Beta stocks to a portfolio. Note that this increase in return occurs without increasing risk because the downside risk has been securely limited by the protective exit stops. In the meantime, the possible upside returns remain unlimited, so using higher Betas pays off by substantially increasing those potential returns.

Of course, investors can’t just randomly add high Beta stocks to a portfolio without doing something to control and limit the risk. The key ingredient to allow this dramatic increase in Alpha is the use of accurate volatility based exits that result in wider stops for high Beta stocks. Then we implement a disciplined position sizing calculation, like the one in our examples, which produces smaller positions for the high Beta stocks.

A final word of caution – investors can’t use the same exits in the high and low volatility stocks unless the algorithm behind those exits factors in the differences in volatility. If stops are used that are not volatility based, the positions in low Beta stocks may be too small and reduce the rewards. If stops are used in the high Beta stocks that are not volatility based, the positions are likely to be too large and too much risk will be taken. If an investors tries too hard to limit risk and makes the common mistake of using a low volatility exit on a high volatility stock they will be unmercifully “whipsawed” as a result of repeatedly getting stopped out too soon and unnecessarily. The alternative mistake of using a high volatility exit on a low volatility stock will be constantly risking much more loss than necessary.

If investors fail to use any protective exits they will have very little, if any, control of risk and they are not adequately protecting their wealth. Without protective stops these unfortunate investors probably lost much more money than necessary last year. If investors need a reliable source of logical and easy to use volatility based exits hey should visit www.SmartStops.net.

In conclusion, by incorporating intelligently adjusting exits and risk based position sizing into one’s investment strategy, it is possible to increase exposure to Beta without increasing risk, and in effect increase Alpha. While historically, risk management solutions focused primarily on rebalancing and diversification, today there is a new breed of risk management solutions that are focused on exits and downside risk management. This article has shown that a combination of effective exits and correct position sizing can allow the use of higher Beta stocks to improve returns without the expected increase in risk. Today, the ability to influence Alpha is a reality.

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