|
| Portfolio |
Market Risk |
Action |
| A |
Client’s market risk (antithetic risk) |
Firm asks client (Corporation, Bank or Retail) to place collateral |
| B |
Firm's market risk by client, client's risk if firm defaults |
Firm’s risk management sets risk limits by client; Client asks firm to place collateral |
| C |
Firm's market risk by portfolio -- risk reduction |
Trading limit control and capital management |
| D |
Firm's Market Risk by Exchange, exchange's risk if firm defaults |
Firm's risk management asks desk for margin, exchange asks firm for margin |
| E |
Firm's market risk by portfolio with exchanges - risk reduction |
Margin management across exchanges |
| F |
Exchange's market risk (antithetic risk)
| Banks are required to set aside capital for potential exposure to an exchange |
|
A portfolio, as defined here, is a group of financial assets held by an individual or by other entities for investment purposes. The assets in a portfolio have a market value and are subject to risk as the market values change.
Portfolios are important both for risk management purposes and for managing the capital requirements needed to support the portfolio. If the portfolio is not managed adequately, not only will the investor lose their capital, but the ability to do further investments. This will also erode the investment advisor’s customer base. The collateral required to support a portfolio is similar to loans needed to fund fixed asset investments with the important exception that the size of the loan varies as the market changes.
Various configurations exist for portfolios, the more well known ones defined by exchanges and their members who bear the risk of default. Collateral exchanges between banks, and collateral requirements by banks from their clients form another source of portfolio risk management. Broker-dealers will use portfolio management for securities lending.
As the venues for investment increase, the benefit of portfolio management also increases due to the diversification benefits. Although each exchange requires margin for the extreme case, within a portfolio that is likely not the case. For example, the margin on a short position in interest rates will be similar to a long position in interest rates, since the worst case is chosen for each within an exchange. In execution, however, the long position in one exchange is likely to offset the short position in another.
The above image provides a range of portfolios by different perspectives. The collateral requirement will be different in each case. In particular, the risk on a long position, using the HVaR/ES standard, will be different from the same position viewed from the counterparty’s perspective, referred to as Antithetic VaR.
The volatility of a portfolio is lower than the sum of the volatility of the underlying assets due to the correlation effect. Consider a portfolio of 2 assets that are 100% negatively correlated. There will be zero risk while this correlation is in effect. A portfolio of 2 assets that are 100% positively correlated will generally have twice the volatility of either). For a 2 asset portfolio, the variance can be measured as A2 + ρAB + B2 where A and B are the volatilities and ρ is the correlation which ranges from -1 to +1. The volatility is the square root of the variance.
The following demonstrates how rebalancing a portfolio by adding a hedge position reduces the overall risk. The portfolio is long shares and offsets the risk by adding a put option. The first graph shows the risk of the shares alone. The second graph shows the risk from the put option alone. For stress analysis a regulatory requirement is to cover risk during a 365 calendar window that includes the worst day over a period up to and including 2007. The stress period for the equity is centered around 12 Nov 2008, and for the put, around 26 Jan 2010. The risk to the long equity position is from a fall and prices, and to the put, a rise in prices. The combining of the two assets results in a different profile. In the combined portfolio, the original risk observation period is still valid since the worst case loss for the two assets together still takes place in the same date range. Click here for more information on observation date requirements.
Click and expand all 3 below to compare unhedged shares, put options, and the combined (hedged) portfolio
The following illustrates the possible risk (in Thousands of dollars), using a 99% confidence interval and 2 day holding period, with at-the-money historical volatility.
There is a significant reduction in the amount at risk. Note that there is a cost to buying this risk protection in the form of option premium. In practice the cost is lowered by purchasing out-of-the money options and various risk vs cost strategies. HVaR is useful for viewing the risk of such strategic portfolios.
|
Current Period VaR |
Current Period ES |
Stress Period VaR |
Stress Period ES |
| 100 AMZN Shares |
-9.08 |
-9.65 |
-21.94 |
-26.61 |
| Puts on 100 AMZN shares |
-3.91 |
-4.98 |
-3.39 |
-5.84 |
| Sum of Risks |
-12.99 |
-14.63 |
-25.33 |
-32.45 |
|
|
|
|
|
| Portfolio Risk |
-4.45 |
-4.7 |
-9.95 |
-11.11 |
Berkshire Hathaway is the world’s largest financial services company by revenue ($210.8 B) Wikipedia org. The U.S. stocks owned by Berkshire Hathaway, as reported to the SEC is updated by CNBC. CNBC Berkshire Hathaway Portfolio Tracker. The portfolio as of Apr 3, 2018, consisted of 47* shares with a total value of $174.3 Billion. The distribution of the top 94% by market value is shown below. The risk profile for each of the stocks (based on 100 shares only) is on RiskSnap's home page.
Buffett's Berkshire suffers $1bn loss after accounting change (source: Financial Times, Eric Platt, May 5, 2018). The company said that new accounting rules meant that the group now had to include unrealised gains and losses on its equity and derivatives portfolio of its earnings which resulted in a $6.4 bn hit to net income. Note that the mix of Berkshire's portfolio as referenced in RiskSnap has no mention of derivatives. This could explain the apparent volatility of BRK price as reflected below in the risk graphs. Perhaps the volatility will reduce when the derivatives (normally hedges) are included.
| Bank of New York Mellon Corp |
|
| Charter Communications, Inc. |
|
| American Airlines Group Inc |
|
| United Continental Holdings Inc |
|
*Remaining shares: Monsanto Company (0.79%),Visa Inc (0.72%),M&T Bank Corporation (0.57%),Mastercard Inc (0.49%),Sirius XM Holdings Inc. (0.49%),Costco Wholesale Corporation (0.45%),Axalta Coating Systems Ltd (0.41%),Synchrony Financial (0.4%),Liberty Global plc - Class A Ordinary Shares (0.36%),Torchmark Corporation (0.3%),Restaurant Brands International Inc (0.28%),Store Capital Corp (0.27%),Teva Pharmaceutical Industries Ltd (ADR) (0.18%),International Business Machines Corp. (0.18%),Liberty Global plc - Class C Ordinary Shares (0.13%),Verisk Analytics, Inc. (0.09%),Sanofi SA (ADR) (0.09%),Walmart Inc (0.07%),Graham Holdings Co (0.04%),Liberty Latin America Ltd (0.03%),Johnson & Johnson (0.02%),Liberty Latin America Ltd (0.01%),Procter & Gamble Co (0.01%),Mondelez International Inc (0.01%),United Parcel Service, Inc. (0.%),Verizon Communications Inc. (0.%)
Following is an analysis based on available market data of the above portfolio and RiskSnap calculations and intended for illustration purposes only
The portfolio was netted for those shares where history covered the period from Feb 2008. Shares where the historical data was insufficient, were not netted. The netted portfolio Expected Shortfall during the stress period was $25.2 billion with worst case being price changes as experienced Jan 20, 2009. The sum of the netted portfolio and the remaining unnetted porfolios results in an Expected Shortfall of $29.1B or a 16.7% drop. This is possibly conservative since no netting is provided for the stocks with not enough history. The ES during the stress period for a single share is $29,000 or slightly less than 10% of the current share price of $296,859 (Apr 3, 2018) , with the worst loss being Nov 19, 2008. The ES loss is consistent with the share price drop of 12%.
The downwards spike of Black Monday 2011 took place Aug 8, 2011 when Standard and Poor's downgraded US sovereign debt from AAA to AA+ where it stands today.
Click and expand both below to compare Risk between the portfolio and the share price BRK-A
