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White Paper: Dollar-Weighted Versus Time-Weighted Returns – Should You Care?

Imagine; you invest $100,000 in a stock. Six months later you put another $100,000 into the same stock. Six months after that you sell all your shares for $300,000. After a few rounds of self- congratulation on your stock picking prowess you decide to calculate your return. You know you invested $200,000 and had gains of $100,000. Since your gain of $100,000 is 50% of the $200,000 invested your gain is 50%. While this is a straightforward calculation something doesn’t feel quite right. Should the fact that only half the money was invested initially with the other half invested midway through the time period cause you to adjust your calculation? In search of answers you go online and find two rate of return calculators. You enter your data and click to the answer. One says you earned 66%, even better than your own calculation had indicated. But the other says your rate of return was… Zero. Yes, zero. Something must be wrong. You recheck your data and determine that both answers are correct. Welcome to the exciting world of dollar-weighted versus time-weighted returns!

Ever since assets have appreciated people have worked hard to come up with methods to quantify their profit. At its simplest, the appreciation calculation is straightforward. Just divide the amount the investment appreciated by the initial value of the investment as in the example above where the $100,000 gain was divided by the $200,000 investment showing a rate of return of 50%.

However it starts getting a bit more complicated if during the period the performance is being measured money is added to or taken from the investment account. Dollar-weighted and time weighted return calculations are the two methods that account for cash inflows and outflows during the performance measurement period.

Let’s look at dollar-weighted returns first. While the calculation is straightforward the details are challenging. All you have to do is divide the gain by the average capital base. Gain is the amount left over after subtracting all the money put into the investment. Average capital base is a bit trickier; it is the sum of the initial investment plus or minus any funds added to or removed from the investment after the start date, adjusted for the time period the funds were in the account.

That’s a tough sentence; here is an example:

Suppose we start our investment account with $100. Six months later we add another $100. Six months after that we want to measure the performance for the previous 12 months. What is the average capital base? It is the initial $100 plus half of the second $100 added to the account, for a total of $150. Only half of the second $100 is included because it was only invested for half the period. If instead of adding funds, $50 had been removed from the account halfway through the performance period, the average capital base would have been $75; the initial $100 minus half of the $50 that was removed.

The advantage to the dollar weighted calculation compared to the basic calculation where gain is divided by the amount invested with no adjustment for cash inflows and outflows is that the dollar weighted calculation modifies the performance to reflect the gain relative to the funds actually available for investment.

Time weighted return takes dollar weighted returns one step further. In calculating time weighted returns, first you divide the performance period into smaller time periods; quarters, months, weeks and days are typical. Then for each of these smaller time periods a dollar weighted return is calculated. Finally, these smaller period returns are compounded to generate the time weighted return for the whole performance period.

Using time weighted returns further diminishes the impact of cash inflows and outflows on the actual return of the assets in the portfolio. A bit of math clarification is in order. When compounding multiple periods of return you must add 1 to each percentage number and then subtract 1 from your final result. Here is why. Suppose you are compounding quarterly and for three quarters in a row you earn 5% per quarter. Mathematically 5% is 0.05 so if we multiply 0.05 * 0.05 * 0.05 we get .0001, or one tenth of one percent. Whenever you multiply any number by a number less than 1 the product will be less than the initial number.

So here is what to do; add 1 to each percentage to be multiplied then subtract 1 from your answer:

1.05 * 1.05 * 1.05 = 1.16
1.16 – 1 = .16 = 16%.
5% per quarter compounds to a 16% total return after three quarters.

So which return calculation makes the most sense? It depends. The basic “gain divided by amount invested” calculation which does not take into account cash inflows and outflows provides the most clarity when you are trying to figure out how many more (or less) dollars you have than you did before investing. But it does not capture the impact of cash moving in and out of the investment account.

Dollar weighted returns capture more than just the return of the assets in the portfolio. They also give you a better idea of the returns earned on the money you had at risk. If your advisor helps you determine when to add funds to the account, or when it makes sense to pull money out, the dollar weighted return is more likely to highlight the impact of that advice. More typically, cash flows into or out of an account are driven by the client and are based on cash flow needs, savings strategy and other life events.

If you want to hone in exclusively on the impact of the investment decisions made within the portfolio then time weighted returns are likely the better measure. However most investors will find that investment portfolios experiencing large inflows and outflows will have time weighted performance that differs from managed portfolios that do not have such contributions and withdraws.

Of course if there are no cash inflows and outflows after the initial investment then all three performance calculation methods; gain divided by amount invested, dollar weighted, and time weighted, will show the same investment return. (great point …. Correct but not intuitively obvious).

Back to that opening problem; why did one performance method show a 66% return while the other showed a 0% return? Here are more details on the twelve months of investing. During the 12 month period the $100,000 investment lost half its value, to $50,000, in the first six months at which point an additional $100,000 was added. In the second six months the investment doubled in value so the $150,000 grew to $300,000.

First we’ll calculate the dollar weighted return which is the gain divided by the average capital base. The gain is $300,000 less the $200,000 that was invested, or $100,000. Next comes the average capital base. We had $100,000 for the full period and $100,000 for half the period for an average capital base of $150,000. $100,000 gain divided by the $150,000 average capital base is .666, or a 66.6% return. Not bad.

Next we’ll calculate the time weighted return and we’ll do it by calculating the dollar weighted return for two time periods and then compounding them. For the first six months the stock declined by $50,000 and the average capital base was $100,000 for a return of -50%. For the second six months the stock appreciated by $150,000 on an average capital base of $150,000 for a return of 100%. To compound these two periods we add 1 to each return and multiply them together:

First, add 1 to each period return;
1 – 50% = .5
1 + 100% = 2

Then multiply the adjusted return numbers together;
2 * 0.5 = 1

Finally, subtract the 1 from your result;
1 – 1 = 0 which equals 0.0%

Performance measurement should be a detailed and accurate exercise following prescribed performance calculation standards. Yet even when the calculations adhere to a standard the results can vary significantly depending on which performance calculation method is used. Next time you’re quoted an investment return you’ll know to ask a few follow-up questions to ascertain what the investment in question might have actually done for you.

John Bird, MBA, CFA, CFP / President
Albion Financial Group
jbird@albionfinancial.com
(801) 487-3700

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Averting Financial Disaster – What You Need to Know

Disaster Waiting to Happen or Disaster Averted; You Choose

Headline: “Earthquake Strikes Salt Lake City. Buildings Destroyed: Utilities Down for a Month”

What comes to mind when we think about disasters are cataclysmic events; floods, earthquakes, fires and the like. And while it is essential to plan for these dramatic possibilities there are far less newsworthy yet much more likely “disasters” that can impact us in adverse ways. So prior to confronting the daunting task of planning for an unlikely large scale disaster spend some time planning for the more likely, and far more mundane, inconveniences that could rock your world. A side benefit to this planning is that your efforts can be used as building blocks when creating a large‐scale disaster recovery plan. Disaster mitigation strategies cover a broad range of topics from planning places for your family to meet in case of an emergency to maintaining adequate supplies of food and water. While the full range of disaster mitigation topics is essential to review, this piece will be limited in scope to essential preparations you should make to avoid crippling problems with your financial affairs.

Have you ever had your purse or wallet lost or stolen?

If so you know well those moments of concern as you attempt to recall exactly what was in it and what damage the thief might do before you are able to take mitigating steps. Having your mail stolen brings the same response with the additional uncertainty of not knowing what exactly was in the mailbox that day. What about that sinking feeling when due to business volatility bank balances are too low at the end of the month to meet your living expenses? Do you have adequate liquidity outside your company if the problem persists? What about your health? Do you have a mechanism in place in the event you are unable to conduct your own affairs due to a temporary disability? Who can you turn to for help in the event of an emergency? Let’s categorize and address these issues.

Checking and Organizing your Financial Information

Begin by organizing your financial data, recording the relevant account information, and storing it in a safe place. Know where your deeds, titles, and insurance policies are located and have them stored securely in a place where you can quickly grab them on your way out the door. Document the possessions in your house; walk through your home with a video camera recording images and describing the contents of each room. If possible have copies of the relevant documents, the video of your home, and account information secured off site and accessible by a trusted friend or advisor who you can reach on short notice. This will prove invaluable should your home be damaged or destroyed and also very useful if putting a hold on your assets or cancelling credit cards or debit cards becomes necessary, particularly if you are out of town and unable to access the information on your own.

Make sure your planning documents are current. This allows for someone you trust to make decisions on your behalf should you be unable to do so. Many of the tools to do this are relatively simple to execute but may have complex repercussions. Be careful to whom you grant these powers. Make sure your health care powers accurately reflect your wishes and are properly executed. Review your estate planning documents whenever you experience a significant life change. Keep copies of critical documents (Social Security, Passport and Driver’s License).

These documents are not very useful if they are not available when needed. Be sure someone you trust knows how to access the documents in case of an emergency. This trusted individual might need to get an executed copy of your health care directive to the hospital should you be unable to do so yourself.

At least annually obtain a credit report from each of the three reporting bureaus. There are also services available that, for a fee, can keep you apprised of any credit activity under your Social Security number on a daily basis.

Maintaining Accessible Rainy Day Funds

The other day when driving to work I pulled into a gas station to fill up. As we all now do, I got out, slid my credit card through the reader, and placed the nozzle in the filler tube. When the pump then told me my card could not be accepted I went inside and was informed that their link was down, they could not accept credit cards, and if I wanted to buy gas I’d have to use cash. Fortunately I had cash that day so was able to fill my tank but while I was doing so a half dozen cashless potential customers were turned away.

We are dependent on our financial system to function each day and the example above indicates how ingrained it has become in the fabric of our lives. While we don’t advocate basing disaster mitigation exclusively around the notion that our financial system will cease functioning it is likely that there could be temporary interruptions to your ability to access funds. This could be a result of a temporary system failure as mentioned above or the result of a failure of the tools in which your funds are invested. To protect against a temporary inability to access funds or credit lines keep several days of cash on hand. These are funds that would tide you over until the financial network in your area is up and running again. It is important to separate this cash from “walking around” cash you may normally carry in your wallet. While it is not the focus of this piece you should also have adequate food and water stored at home to tide you through a temporary period of time in the event you are unable to purchase basic supplies.

Far more likely than a systemic financial failure is an event specific to you or your region of the country that interrupts your usual cash flows from employment. Have a cash reserve set up to carry you and your family through three to six months of lean times. Keep these cash reserves as safe and liquid as possible. FDIC insured bank deposits and high quality money market funds are the best options. Yes, the yields on these tools are nonexistent right now but the purpose of this piece of your financial puzzle is safety and liquidity, not return.

Be careful of investment tools that are “similar” to money market funds but may offer a slightly higher current yield. While many of these tools may function as advertised for years, failure is most likely to occur in a time of crisis; just when you need it most. Auction rate securities, for example, were very popular as a cash management tool several years ago. By trading daily liquidity for weekly liquidity investors received a higher interest rate on their money. Unfortunately many investors in these tools did not understand that these were not money market funds. In 2008 when buyers for auction rate securities dried up holders were unable to sell their positions for much needed cash.

Check your insurance coverage. A good disability policy can make a big difference for you and your family should you be rendered unable to work for a period of time. Good health insurance (and yes, we recognize this is a hot button issue) can make the difference between a health issue being a minor setback or a road to bankruptcy. As CEO you are likely the primary breadwinner in your household. What happens to your family if you pass away? Life insurance, properly used, can really help your family meet their objectives should you be unable to provide for them.

The last point about liquidity is to review whether your financial assets are adequately diversified. It is very common for CEO’s, business owners, and senior executives to have the majority of their net worth tied up in their company. While wealth is often best created through concentration it is best retained through diversification. When your paycheck, your career path, much of your net worth, and in many cases your reputation is tied to a single company it is prudent to diversify a portion of your balance sheet away from that company. There are many tangible benefits to building a substantial portion of your net worth outside your company. These include the flexibility to raise funds without impacting your firm and the ability to maintain your family should the company fall on rough times and be unable to meet your cash flow needs. It also provides a lifeboat should the unthinkable happen and the company fail.

The Benefits of a Good Team

You likely already work with an accountant, an attorney and a financial advisor. When creating your disaster mitigation plan do not hesitate to take advantage of their expertise. A solid team watching your back can not only ease the process of creating your plan but can certainly prove invaluable help should the plan ever be called into use.

Your attorney can help you correctly create legal documents, specific to you, that provide essential guidance and a framework for action in the event of a variety of disasters. He can work through asset titling issues to ensure that your assets are held in such a way that they provide the most benefit to you and your family in a variety of prospective circumstances. Your attorney can review your full slate of documents from trusts and wills to medical and financial powers to make sure they meet your current requirements and do not have conflicting passages that could cause problems in the future.

Additionally, your attorney will usually keep a copy of all documents they create giving you the benefit of off‐site storage for these critical items should your originals become lost, stolen or destroyed. In addition to advice on how best to navigate the tax and regulatory environment in which your business operates your accountant is an excellent backup location for your specific financial information. Should your financial information be lost, stolen, or destroyed your CPA will have records that can provide essential guidance as the data is reconstructed. Often your CPA firm will know your corporate information as well as your personal information and can be an excellent source of aid in the event a disaster befalls your firm.

Most CEO’s of closely held businesses keep close tabs on most if not all of the financial relationships of their company and some choose to forego an accounting relationship altogether, preferring to handle these functions on their own. While this can be effective for the individual CEO it quickly becomes a problem if the CEO is no longer able to function. It can be extremely disruptive to the business, to say nothing of the family members charged with picking up the pieces, to recreate this knowledge base in the absence of a quality, previously involved, CPA.

Often communications with your financial advisor occur with far more frequency than with the other professionals on the team. It is in your best interest to use that relationship to its fullest. Your financial advisor can serve as a trusted backstop if they know you, the pieces of your financial puzzle, and how you’d like the pieces to fall together in the coming years. They can be an excellent place to keep backup copies of your data, and if they adhere to a fiduciary standard, can give you the security of knowing there is a team out there that has a duty to look out for your best interests first. Your financial advisor can provide guidance regarding tools and techniques that are best suited to your individual circumstances whether it be a place to park an emergency reserve fund or the appropriate investment policy for financial assets with a longer time horizon. In the event of an emergency they are in a position to quickly help you implement steps to mitigate the damage to your financial situation.

Disaster recovery planning can be a daunting project but like so many endeavors it can be accomplished if divided into smaller more manageable tasks. The items outlined here are some of the steps that serve as building blocks to a comprehensive disaster mitigation plan. There are scores of resources available to help you design and build your own disaster recovery strategy. One of the most comprehensive sources is the Federal Emergency Management Agency. They have extensive guidance available online at http://www.fema.gov/plan/index.shtm. May you create an excellent plan and never have to use it.

Devin Pope, MBA, CFP
Senior Wealth Advisor
dpope@albionfinancial.com
Albion Financial Group
(801) 487-3700