Volatility Analysis for Portfolio 'WIP'

This analysis evaluates the volatility of a portfolio from recent daily price data. It then considers the effect on volatility of buying and selling each security (stock, bond, or mutual fund) in the portfolio. The result is used to suggest possible trades that would have resulted in portfolios with lower volatility. One can infer that making those trades in the present will have a similar effect on the portfolio's future volatility. One can also infer that portfolios with low daily volatility will have low volatility over longer periods of time.

For most securities the plot of shares traded vs. portfolio volatility has a 'W' shaped curve as can be seen below. The central peak represents the portfolio volatility when the security is not held. The right valley in the curve represents the optimum long exposure to the security and the left valley represents the optimum short exposure. The outer legs represent over-exposure to the security. This curve is shifted left or right by the amount presently owned. It can be tilted or lopsided depending on the security and its interaction with the rest of the portfolio.

Choosing trades from among those suggested will generally result in a better-diversified portfolio. This is not a recipe for instantly optimizing a portfolio. In fact, at most one trade should be selected from the suggestions. The analysis should then be repeated on the changed portfolio to consider further trades. This analysis is a tool, to be used with other tools, and the investor's judgment, to make investment decisions over time. It is possible to have a well-diversified portfolio that consistently loses money; it will just do it with low volatility.

This analysis is related to Modern Portfolio Theory in that the suggested trades will always move the portfolio leftward on a risk-return chart, that is, closer to the efficient frontier. The analysis does not consider expected returns of securities, because expected return is difficult to determine from historical data (or any other known method). The analysis only considers volatility, which is related to risk and variability of expected return, since volatility can be more reliably determined from historical data. Since the analysis does not consider expected return, it is useful to a variety of investment styles, including value, growth, and momentum.

The analysis also lists the significant correlations for each security in the portfolio with every other security and with the portfolio value and with the S&P500 index. Correlation is measured by the correlation coefficient between the daily percentage price changes, which varies from -1 to 1. Negative coefficients are rare in practice, except between a large short position and the portfolio value. Correlations with coefficients between -0.3 and 0.3 are considered insignificant and ignored.

The correlation information can be useful for discovering multiple trades that reduce portfolio volatility. For example, assume that securities A an B are strongly correlated, and both held long in the portfolio. Assume also that the investor wants to buy more of security A, but doing so would increase the portfolio volatility. Since they are correlated, selling some of security B may allow buying more of security A without increasing volatility. Also, strongly correlated securities are good candidates for paired short/long trades that can reduce volatility.

The analysis can only consider the securities that are included in the portfolio. It cannot suggest diversification into securities that are not included. Securities can be included, even if they are not currently held, by entering 0 shares held. If a security is held long, the analysis will not suggest trades that result in a short position. Similarly, it will not suggest trades that more than cover a short position.

The portfolio is listed here. Short positions have negative shares held. For securities not held, "0L" indicates that it is a potential long position and "0S" indicates that it is a potential short position.

Ticker Symbol | Shares Held |

ARQL | 0L |

BCHE | 8000 |

CPRO | 30000 |

CSCO | 3000 |

DURA | 4000 |

DWTI | 0L |

FRTE | 15000 |

FSON | 45000 |

INTC | 2000 |

KLAC | 3500 |

MMCN | 7500 |

ORCL | 5000 |

PFE | 1500 |

FON | 2750 |

RMDY | 7500 |

SANM | 1750 |

YHOO | -1500 |

Price data was analyzed for **120** trading sessions from **03/11/98** to **08/31/98**.
Verify that the Historical Price Data for this portfolio is correct.

This portfolio has volatility **1.207**.
This compares with the S&P500 Index volatility **1.054**.
The volatility measure used in this analysis is the
standard deviation of the daily percentage price change,
with some minor adjustments.
The correlation coefficient between daily percentage price changes of the
portfolio value and the S&P500 index is **0.614**.

Stock **ARQL** has volatility **3.974**.
It is not currently held in the portfolio. Its latest price is **4.650**.

Trade suggestions: |
Buying 12300 shares reduces volatility to 1.169, a 3.1% improvement. |

Buying 24600 shares reduces volatility to 1.185, a 1.9% improvement. |

No significant correlations.

Stock **BCHE** has volatility **2.156**.
Portfolio holds **8000** shares at latest price **15.406**, representing **7.2%** of money-at-risk.

Trade suggestions: |
Selling 3700 shares reduces volatility to 1.205, a 0.1% improvement. |

This stock is correlated with Portfolio Value (0.620) , S&P500 Index (0.478) , MMCN (0.452) , INTC (0.381) , CSCO (0.372) , KLAC (0.326) , DWTI (0.319) , RMDY (0.315) , DURA (0.314) , FON (0.302) .

Stock **CPRO** has volatility **9.317**.
Portfolio holds **30000** shares at latest price **0.780**, representing **1.4%** of money-at-risk.

No trade suggestions.

No significant correlations.

Stock **CSCO** has volatility **1.494**.
Portfolio holds **3000** shares at latest price **87.722**, representing **15.3%** of money-at-risk.

Trade suggestions: |
Buying 1000 shares reduces volatility to 1.201, a 0.5% improvement. |

Buying 2000 shares reduces volatility to 1.197, a 0.9% improvement. | |

Buying 3000 shares reduces volatility to 1.194, a 1.1% improvement. | |

Buying 4000 shares reduces volatility to 1.192, a 1.2% improvement. | |

Buying 5000 shares reduces volatility to 1.191, a 1.3% improvement. | |

Buying 6000 shares reduces volatility to 1.191, a 1.3% improvement. |

This stock is correlated with Portfolio Value (0.693) , S&P500 Index (0.544) , MMCN (0.500) , YHOO (0.496) , KLAC (0.456) , SANM (0.450) , RMDY (0.434) , INTC (0.433) , ORCL (0.413) , FRTE (0.388) , BCHE (0.372) , PFE (0.357) .

Stock **DURA** has volatility **2.456**.
Portfolio holds **4000** shares at latest price **16.769**, representing **3.9%** of money-at-risk.

No trade suggestions.

This stock is correlated with Portfolio Value (0.474) , DWTI (0.444) , RMDY (0.422) , INTC (0.360) , S&P500 Index (0.358) , BCHE (0.314) , MMCN (0.304) .

Stock **DWTI** has volatility **3.674**.
It is not currently held in the portfolio. Its latest price is **2.931**.

No trade suggestions.

This stock is correlated with DURA (0.444) , Portfolio Value (0.369) , BCHE (0.319) , MMCN (0.307) .

Stock **FRTE** has volatility **3.695**.
Portfolio holds **15000** shares at latest price **3.272**, representing **2.9%** of money-at-risk.

No trade suggestions.

This stock is correlated with Portfolio Value (0.413) , CSCO (0.388) , MMCN (0.332) .

Stock **FSON** has volatility **4.117**.
Portfolio holds **45000** shares at latest price **3.112**, representing **8.2%** of money-at-risk.

**Warning**: this stock is lightly traded. Its volatility may not reflect
the underlying risk. Trade with caution.

No trade suggestions.

This stock is correlated with Portfolio Value (0.347) .

Stock **INTC** has volatility **1.671**.
Portfolio holds **2000** shares at latest price **73.778**, representing **8.6%** of money-at-risk.

Trade suggestions: |
Buying 800 shares reduces volatility to 1.204, a 0.3% improvement. |

Buying 1600 shares reduces volatility to 1.201, a 0.5% improvement. | |

Buying 2400 shares reduces volatility to 1.200, a 0.6% improvement. | |

Buying 3200 shares reduces volatility to 1.200, a 0.6% improvement. | |

Buying 4000 shares reduces volatility to 1.200, a 0.6% improvement. | |

Buying 4800 shares reduces volatility to 1.201, a 0.5% improvement. |

This stock is correlated with Portfolio Value (0.642) , KLAC (0.610) , SANM (0.562) , S&P500 Index (0.502) , CSCO (0.433) , ORCL (0.413) , BCHE (0.381) , PFE (0.367) , DURA (0.360) , FON (0.350) , RMDY (0.330) .

Stock **KLAC** has volatility **2.793**.
Portfolio holds **3500** shares at latest price **23.084**, representing **4.7%** of money-at-risk.

Trade suggestions: |
Selling 2500 shares reduces volatility to 1.197, a 0.8% improvement. |

This stock is correlated with INTC (0.610) , Portfolio Value (0.572) , SANM (0.467) , CSCO (0.456) , YHOO (0.416) , S&P500 Index (0.380) , ORCL (0.344) , BCHE (0.326) , PFE (0.311) .

Stock **MMCN** has volatility **3.793**.
Portfolio holds **7500** shares at latest price **18.600**, representing **8.1%** of money-at-risk.

Trade suggestions: |
Selling 6200 shares reduces volatility to 1.113, a 7.8% improvement. |

Selling 3100 shares reduces volatility to 1.157, a 4.1% improvement. |

This stock is correlated with Portfolio Value (0.722) , CSCO (0.500) , RMDY (0.480) , BCHE (0.452) , S&P500 Index (0.446) , YHOO (0.359) , FRTE (0.332) , FON (0.330) , DWTI (0.307) , DURA (0.304) .

Stock **ORCL** has volatility **1.949**.
Portfolio holds **5000** shares at latest price **20.744**, representing **6.0%** of money-at-risk.

Trade suggestions: |
Buying 2800 shares reduces volatility to 1.196, a 0.9% improvement. |

Buying 5600 shares reduces volatility to 1.188, a 1.6% improvement. | |

Buying 8400 shares reduces volatility to 1.183, a 2.0% improvement. | |

Buying 11200 shares reduces volatility to 1.181, a 2.2% improvement. | |

Buying 14000 shares reduces volatility to 1.180, a 2.2% improvement. | |

Buying 16800 shares reduces volatility to 1.181, a 2.1% improvement. |

This stock is correlated with Portfolio Value (0.435) , INTC (0.413) , CSCO (0.413) , KLAC (0.344) , S&P500 Index (0.301) .

Stock **PFE** has volatility **1.639**.
Portfolio holds **1500** shares at latest price **96.878**, representing **8.5%** of money-at-risk.

Trade suggestions: |
Buying 600 shares reduces volatility to 1.195, a 1.0% improvement. |

Buying 1200 shares reduces volatility to 1.185, a 1.9% improvement. | |

Buying 1800 shares reduces volatility to 1.176, a 2.6% improvement. | |

Buying 2400 shares reduces volatility to 1.169, a 3.1% improvement. | |

Buying 3000 shares reduces volatility to 1.164, a 3.6% improvement. | |

Buying 3600 shares reduces volatility to 1.159, a 4.0% improvement. |

This stock is correlated with Portfolio Value (0.459) , S&P500 Index (0.457) , INTC (0.367) , CSCO (0.357) , FON (0.324) , KLAC (0.311) .

Stock **FON** has volatility **1.139**.
Portfolio holds **2750** shares at latest price **68.828**, representing **11.0%** of money-at-risk.

Trade suggestions: |
Buying 900 shares reduces volatility to 1.186, a 1.7% improvement. |

Buying 1800 shares reduces volatility to 1.168, a 3.3% improvement. | |

Buying 2700 shares reduces volatility to 1.151, a 4.7% improvement. | |

Buying 3600 shares reduces volatility to 1.135, a 6.0% improvement. | |

Buying 4500 shares reduces volatility to 1.121, a 7.1% improvement. | |

Buying 5400 shares reduces volatility to 1.108, a 8.2% improvement. | |

Buying 6300 shares reduces volatility to 1.097, a 9.1% improvement. |

This stock is correlated with Portfolio Value (0.433) , S&P500 Index (0.430) , INTC (0.350) , MMCN (0.330) , PFE (0.324) , RMDY (0.319) , BCHE (0.302) .

Stock **RMDY** has volatility **3.697**.
Portfolio holds **7500** shares at latest price **9.615**, representing **4.2%** of money-at-risk.

Trade suggestions: |
Selling 5900 shares reduces volatility to 1.167, a 3.3% improvement. |

This stock is correlated with Portfolio Value (0.596) , MMCN (0.480) , S&P500 Index (0.463) , CSCO (0.434) , DURA (0.422) , YHOO (0.375) , INTC (0.330) , FON (0.319) , BCHE (0.315) , SANM (0.307) .

Stock **SANM** has volatility **2.702**.
Portfolio holds **1750** shares at latest price **33.256**, representing **3.4%** of money-at-risk.

No trade suggestions.

This stock is correlated with INTC (0.562) , KLAC (0.467) , CSCO (0.450) , S&P500 Index (0.443) , Portfolio Value (0.438) , YHOO (0.378) , RMDY (0.307) .

Stock **YHOO** has volatility **3.148**.
Portfolio holds **1500** shares **short** at latest price **75.162**, representing **6.6%** of money-at-risk.

Trade suggestions: |
Selling 4800 shares reduces volatility to 0.931, a 22.9% improvement. |

Selling 4000 shares reduces volatility to 0.957, a 20.8% improvement. | |

Selling 3200 shares reduces volatility to 0.990, a 18.0% improvement. | |

Selling 2400 shares reduces volatility to 1.031, a 14.5% improvement. | |

Selling 1600 shares reduces volatility to 1.081, a 10.4% improvement. | |

Selling 800 shares reduces volatility to 1.140, a 5.6% improvement. |

This stock is correlated with CSCO (0.496) , Portfolio Value (0.428) , S&P500 Index (0.417) , KLAC (0.416) , SANM (0.378) , RMDY (0.375) , MMCN (0.359) .

Copyright © 1998 A. Peter Allan. All rights reserved.