Showing posts with label portfolio returns. Show all posts
Showing posts with label portfolio returns. Show all posts

Friday 28 April 2017

Measures of Returns


  1. Holding period return
  2. Arithmetic or mean return
  3. Geometric mean return
  4. Money-weighted return
  5. Annualised return
  6. Return on a portfolio 
  7. Gross versus Net Returns
  8. Pre-Tax versus After-Tax Nominal Returns
  9. Real versus Nominal Returns
  10. Leveraged Return

Tuesday 22 November 2016

The Different Methods For Measuring Overall Portfolio Returns



Ever wonder why your brokers profit and loss statements don’t always add up with your calculations? This normally due to the different methods of measuring overall portfolio returns.

In this article we are going to discuss two of the most commonly used methods which you can apply to your portfolio holdings, that of the money-weighted rate of return and that of the time weighted rate of return. Both methods are officially recognised by the CFA charter.

Let’s start with the money-weighted rate of return. This method takes into account all cash inflows and outflows of a portfolio and gives a defined measure of the internal rate of return (IRR). Any money added at the beginning of the account is considered a money inflow, and all money withdrawn from the account as well as the remaining balance at the end of the period are considered outflows.measuring overall portfolio returns

We can use a basic model to illustrate what this means. Suppose an investors buys 1000 stocks of Vertu Motors at the beginning of the period for 30p each. After 1 year the investor still likes the stock and decides to buy another 1000, only this time the price is now 35p a share. At the end of year two the investor sell all 2000 of the stocks for 45p a share, additionally at the end of each period Vertu paid a 3p dividend on each stock.measuring overall portfolio returns

So
At T=0 1000 shares were bought at 30p a share, meaning a cash inflow of +£300
At T=1 another 1000 shares were purchase for 35p a share, however a £30 dividend was also paid, meaning a cash inflow of (1000 x 0.35) – 30 = +£320
At T=2 they sold all their shares for 40p a share, and received a 3p dividend on the 2000 shares, meaning (2000 x 0.4) + (2000 x 0.03) = -£860
From this we have our cash flow time series
CF0 = +£300
CF1 = +£320
CF2 = -£860

The formula for working out the final return does look a little scary:
£300 + (£320/(1+r)) = (860/(1+r)²)
Fortunately we live in a world where there are plenty of online resources that will work this out for us. I personally like to use a financial calulator to input cash flows from a time series to work out the IRR. The answer to this formula is
24.18% overall return

Now let’s see what happens when we use the time weighted rate of return to measure the portfolio’s actual return. Time weighted method has the benefit of measuring compound growth.

To do this we need to measure each individual holding periods growth. In the above example we have 2 holdings periods, year 1 and year 2.

Holding period 1: Beginning value = £300
Dividends paid = £30
End Value = £350 (1000 shares x 35p)
HPR1 = ((£350 + £30) / £300) – 1 = 26.66%

Holding period 2: Beginning value = £700 (2000 x 35p)
Dividends paid = £60
End Value = £800 (2000 shares x 40p)
HPR2 = ((£800 + £60) / £700) – 1 = 22.86%

Now that we have both these figures we need to find the total compounded annual growth rate that would have produced the total return that equals the return over the 2 holding periods. The formula for this is:
(1+ time-weighted rate of return)² = (1.2666)(1.2286)
We can rearrange this to get:
time-weighted rate of return = √((1.2666)(1.2286)) – 1
= 24.47% overall return

As we can see both methods are considered correct, yet they yield different results. Although the difference is negligible, this was only demonstrated across a small sample portfolio. The larger the cash flows, the wider the differences in measurements will be.

As a rule the time weighed rate of return is considered superior as money weighted returns can be influenced by timing. Measuring money weighted returns before a period of relatively high returns will return a higher figure and can therefore be ‘massaged’.


http://articles.roburir.com/different-methods-measuring-overall-portfolio-returns/

Monday 1 July 2013

The relationship of risk and potential reward in stock investing is often misunderstood in shaping an investment strategy.

There is no investing in stocks without risk and there is no return without risk.

If you are adverse to the idea of taking any amount of risk, then stocks are not for you.

It will be more difficult (but not impossible) for you to reach your financial goals without investing in stocks.


Understanding Risk

Risk is the potential for your investment to lose money, for a variety of reasons - meaning your stock's price will fall below what you paid for it.

No one wants to lose money on an investment, but there's a good chance you will if you invest in stocks.

The rule of thumb is "the higher the risk, the higher the potential return, and the less likely it will achieve the higher return."

Buying a stock that is risky doesn't mean you will lose money and it doesn't mean it will achieve a 25% gain in one year. However, both outcomes are possible.

How do you know what the risk is and how do you determine what the potential reward (stock price gain) should be?


Measuring risk against reward

When you evaluate stocks as potential investment candidates, you should come up with an idea of what the risks are and how much of a potential price gain would make the risks acceptable.

Calculating risk and potential reward is as much an art as it is a science.

You need to understand the principle of risk and reward to make an educated investment as opposed to a guess.

The most common type of risk is the danger your investment will lose money.

You can make investments that guarantee you won't lose money, but you will give up most of the opportunity to earn a return in exchange.

When you calculate the effects of inflation and the taxes you pay on the earnings, your investment may return very little in real growth.


Will I achieve my financial goals?

If you can't accept much risk in your investments, then you will earn a lower return.

To compensate for the lower anticipated return, you must increase the amount invested and the length of time it is invested.

Many investors find that a modest amount of risk in their portfolio is an acceptable way to increase the potential of achieving their financial goals.

By diversifying their portfolio with investments of various degrees of risk, they hope to take advantage of a rising market and protect themselves from dramatic losses in a down market.

The elements that determine whether you can achieve your investment goals are the following:
1. Amount invested
2. Length of time invested.
3. Rate of return or growth
4. Fewer fees, taxes, and inflation.


Minimize risk - Maximize reward

The MOST SUCCESSFUL INVESTMENT is one that gives you the most return for the least amount of risk.

Every investor needs to find his or her comfort level with risk and construct an investment strategy around that level.

A portfolio that carries a significant degree of risk may have the potential for outstanding returns, but it also may fail dramatically.

Your comfort level with risk should pass the "good night's sleep" test, which means you should not worry about the amount of risk in your portfolio so much as to lose sleep over it.

There is no "right or wrong" amount of risk - it is a very personal decision for each investor.

However, young investors can afford higher risk than older investors can because young investors have more time to recover if disaster strikes.

If you are 5 years away from retirement, you don't want to be taking extraordinary risks with your nest-egg, because you will have little time left to recover from a significant loss.

Of course, a too-conservative approach may mean you don't achieve your financial goals.

Wednesday 5 September 2012

Stocks and Bonds: Risk vs. Return



Take a good look at this chart.

It is a portfolio consisting of only 2 assets:  stock and bond.  

Here are some interesting points:  

1.  100% in Stock
This portfolio has the highest risk and also probability of the highest return.

2.  100% in Bond
This portfolio has low risk (NOTE: NOT THE LOWEST) and has lower return.

3.  50% in Stock and 50% in Bond
This portfolio has the same risk as and has higher return than the portfolio that is 100% in Bond.

4.  25% in Stock and 75% in Bond
This portfolio has the lowest risk and has higher return than the portfolio that is 100% in Bond.


(You may assume that holding cash giving an interest rate of 3% is the equivalent of holding a bond with a coupon rate of 3%.)


Conclusion:

Holding 100% in bond carries the same risk as holding 50% in stock and 50% in bond.  However, the probability of a higher return for the same risk should make investors favour holding 50% in stock and 50% in bondthan to hold 100% in bond.

For those who are very risk averse, for example in the present falling market, the lowest risk is the portfolio that is 25% stock and 75% bond, and not the portfolio that is 100% in bond.  Moreover, the portfolio that is 25% stock and 75% bond, offers a probability of higher return for lower risk, that the portfolio with 100% in bond.

Monday 16 April 2012

Why your portfolio may not be as healthy as you think

Why your portfolio may not be as healthy as you think
Quarterly statements rarely tell the whole story
By Tom McFeat, CBC News Posted: Feb 27, 2012 5:36 AM ET

You can scan your quarterly statements for mention of your personal rate of return, but you may not find it. Many investment advisers and firms don't routinely provide it. (iStock)

You've just received the quarterly statement from your mutual fund company or financial adviser, and the results seem good. Your portfolio's worth has grown by five per cent from the last quarter and by 15 per cent over the past year —in fact, you see that your portfolio has doubled in the past five years.
Wow, you think, my financial adviser is a genius!
Not so fast.
Chances are that the figures you've been provided with show the overall value of your investment holdings. The catch is that most statements don't clearly show how that figure has been inflated by your regular contributions and perhaps by regular deposits of interest.

Warren MacKenzie, CEO of Toronto-based Weigh House Investor Services, says that when he worked at a big mutual fund company 20 years ago, he suggested they provide clients with calculations of their personal rate of return rather than the overall growth of their portfolio.In other words, that seemingly glowing return on your investments could be due in large part to the additional contributions you've made, not to growth of the investments themselves.
"'Great idea,'" they said. 'We'll get right on it.'"
Twenty years later, he's still waiting.

Common error

To figure out the real performance of your portfolio, you have to account for all those deposits (and any withdrawals). Failing to do that will leave you with a wildly inaccurate picture of how your investment portfolio has been doing.
It sounds simple, but it's surprising how often this factor is overlooked.
Back in the 1990s, a group of women investors from Beardstown, Ill., realized they'd made this mistake – but not before they'd written a best-selling book about how their small investors club had beaten the stock market and produced an annualized return of 23.4 per cent over 10 years. The book crowed about how their approach to investing delivered results that far surpassed what most professional money managers had been able to achieve.
The only trouble was, they had forgotten to account for those cash inflows into their club. The investment growth of their portfolio over those 10 years was actually just 9.1 per cent annually — six percentage points lower than what the broad market had returned.
Embarrassing doesn't begin to describe the fallout. Their well-meaning but hopelessly inaccurate bestseller — The Beardstown Ladies Common-Sense Investment Guide: How We Beat the Market and How You Can Too — was pulled from store shelves just as the lawsuits began to fly.

Rate of return

So, how do you avoid the Beardstown fiasco and figure out how you'rereally doing financially?
What you need to calculate is your own internal rate of return (IRR) — also known as the personal rate of return or the dollar-weighted rate of return.
What you need to calculate is your own internal rate of return (IRR) — also known as the personal rate of return or the dollar-weighted rate of return.
You can scan your quarterly statements for a mention of this figure, but you may not find it. Many advisers and firms don't routinely provide it.
Why not?
Well, that would make it easier to compare just how well your portfolio has done relative to an appropriate benchmark, such as the average return of the markets. Some advisers, it seems, don't want their clients to know the ugly truth that they aren't adding much, if any, value for the fees they charge.
MacKenzie has witnessed first-hand how reluctant some advisers are to reveal how well (or poorly) their clients are actually faring compared to the benchmark.
"One woman who came to see us said her adviser told her that [calculating her benchmark] couldn't be done because she had both stocks and bonds," he said.
The bottom line quickly became clearer, said MacKenzie, when his own calculations showed the adviser had badly underperformed the benchmark.
"I think he's afraid he'll lose the account if he comes clean," MacKenzie said.

Figuring it out

Figuring out one's personal rate of return in a portfolio is not the easiest calculation to perform, especially for the mathematically challenged. MacKenzie's firm has an online calculator that will do the figuring for you.
"It's the best one I've seen on the web that's free," says Justin Bender, a portfolio manager at PWL Capital, a fee-based investment management firm.
Bender cautions that large contributions made just before periods of relatively good or poor performance can skew the results. But for most investors, he says, the Weigh House calculator works well.
"A lot of advisers like to pretend that active management is paying off," says Bender.
The calculator can reveal the truth — that most advisers don't outperform benchmarks over the long term.
Besides its rate of return calculator, Weigh House also has calculators that can figure out if your portfolio's performance is falling short of the appropriate benchmark. One has users spell out their asset mix and compares that with appropriate benchmarks, so if their portfolio is 50 per cent equities and 50 per cent fixed income, they won't be comparing returns to an all-equity benchmark.
A third calculator tells you how much underperformance can cost you over time. Seeing how relatively small changes in the rate of return can have a huge impact on how much money you'll have in your golden years is sobering stuff, and it leads you to wonder why there isn't a requirement to routinely disclose this information.

Adviser fees don't always translate into profits

FAIR Canada — the Canadian Foundation for Advancement of Investor Rights — supports moves to have the industry provide better performance information to investors.
'Many investors find after 10 years that they're no further ahead than when they started.'— Ermanno Pascutto, Canadian Foundation for Advancement of Investor Rights
"Performance reporting has not been particularly uniform," says the group's executive director, Ermanno Pascutto, noting that sometimes such reporting is non-existent.
"Many investors find after 10 years that they're no further ahead than when they started, but the financial adviser has generated large fees."
That makes it even more critical, he says, that investors be given easy-to-understand information about how their portfolio has been doing so they can see whether their advisers have been earning those fees.
Still, some firms are coming through. BMO InvestorLine and RBC Direct Investing are two discount brokerage firms that routinely provide their do-it-yourself clients with personal rate of return calculations. Investment counsellors often do this for their high-net-worth clients. But many other firms that actively manage money don't routinely do this, nor do most financial planners.
What should you do if your adviser says he or she can't — or won't — provide this calculation for you?
"Find a new adviser," says MacKenzie. "In most cases, they won't volunteer it. But in most cases, if you ask, you can get it."

Portfolio Accounting


Portfolio Accounting

A basic understanding of 'portfolio accounting' is necessary when wanting to calculate returns. Portfolio accounting is also very important when it comes to dealing with derivatives. Most of what will follow in this subchapter looks trivial, but can give one or two headaches in practical applications.
'Portfolio accounting' is about recording, classifying, and summarizing financial events that affect an investment portfolio.

Portfolio Definition

Although it might sound trivial, the definition of individual 'portfolios' isn't always that straight-forward in practice.
We shall define a 'portfolio' as an abstract accounting entity including at least one security and one cash account. The term 'abstract' merely points to the fact that this definition does not necessarily correspond to 'real-world' accounting entities.

Basic Relationships

The relationships below are expressed on a "net" basis (net of transactions costs, fees & withholdings taxes).
Ending Market Value = Beginning Market Value
                                     + Net Contributions
                                     + Gains&Losses
Net Contributions = Contributions - Withdrawals
G&L = Income
           + Net Capital Gains&Losses
Net Capital Gains&Losses = Sales - Purchases
                                             + Ending Market Value Securities
                                             - Beginning Market Value Securities
Ending Cash Balance = Net Contributions + Income + Sales -Purchases
Note that for return calculation purposes, "gains and losses" are defined on a 'beginning-of-calculation-period market value basis', and not on a 'cost basis' as in an accounting context. The differences between the two concepts of "gains and losses" are...
  • Valuation: Accounting G&L are calculated based on cost prices at the time each security was purchased. When calculating investment returns, all securities are considered at theirmarket prices.
  • Time Period: In calculating accounting G&L, the holding period of securities are relevant (because different holdings periods are mixed, an inventory model such as LIFO has to be specified additionally. The calculation of investment returns refers to a specific calendar period (for example, "monthly")and stocks and flows during this period only are relevant.
The further decomposition of "net gains and losses" in "realized" and "realized" components is not of particular interest for return calculation purposes. The only thing to remeber is not to include 'realized gains & losses' as 'income' when calculating investment returns: As realized gains & losses are reinvested, this would result in double-counting and therefore distortion of investment returns.
Market values must be calculated including accruals.
The above portfolio accouting realtionships can be illustrated graphically...

Click here for a large version of the above chart.


Market Valuation

Portfolios are valued at market prices ('Mark-to-Market').
Accruals should be reflected in market prices whenever possible. Accrual accounting is a must for fixed-income securities, but typically rather unimportant in the context of dividends on equity. Dividends are not payable unless the stock was owned on the record date, so dividends are accrued as income on valuation dates  from the ex-dividend date up to the payable date trade.
Valuation issues are a very important, but often neglected issue in return calcuation and therefore in investment performance analysis: 'garbage in, garbage out'.
Mark-to-Market versus Mark-To-Model, Mark-to-Market versus OTC...
For illiquid instruments, there is no market price available and MTM can become a serious problem. The choice of valuation model is very often under the control of asset managers. They can therefore take advantage to manipulate the prices so as to smooth the portfolio returns. If this is the case, the auto-correlation coefficient of the portfolio return series will be significant. As a result, volatility of returns (=risk) will be underestimated as well as the correlation of the fund with peer products or the benchmark. The diversification benefits of the portfolio to the investor will therefore be overestimated.

Cash Flows

Income (dividends, coupons) is included in return calculations if income is re-invested. Income is an internal cash flow. Selling/buying securities also generates internal cash flows (transfer of value from securities to cash account or vice versa)
Contributions and withdrawals are external cash flows. For convenience reasons, we use the summary term 'net contributions', defined as contributions minus withdrawals.
Some authors use the term 'cash flow' instead of net contributions. This can easily lead to confusion when mixing up internal with external 'cash flows'. We strongly recommend avoiding the term 'cash flow' in the context of return calcuations and substitute it with the relevant conpcets directly (income, contributions etc.)
Besides actual client orders, there exist other external cash flows (especially withholding taxes, fees). When presenting net contributions, customer orders and other external cash flows should be reported as separate line items.

Taxes

Terminology: 'after-tax' and 'before-tax' returns.
Difficult to generalize since tax rates are customer specific.
In the context of a specific portfolio, returns are normally stated on a 'before-tax' basis, where values are not subject to any deductions in respect of tax (whether incurred or not). Any payments to the tax office out of the portfolio are then treated as a withdrawal of funds. When calculating returns after taxes, tax payments outside the portfolio have to considered as contributions.
Reclaimable (withholding) taxes versus non-reclaimable taxes: any reclaimable taxes payed have to be consdiered as withdrawals. Reclaimable taxes received are contributions.

Fees

Investment fee structures differ significantly across countries and products. In a universal bank setting, for example, investors might use one bank for all investment management services. Such full-service providing banks might work with cross-funded (subsidized) fees, partially bundled or summed up to an all-inclusive fee (also known as wrap account programs). In the case of a wrap account, 'net-of-fee performance' would mean a net-of-management-and-brokerage/custody-fee performance while in a difference setting, 'net-of-fee performance' is understood as net ofmanagement fees only.
Such differences complicate net-of-fee performance calculations considerably and also affect comparability of returns within a company (aggregating different types of clients and accounts to composites) and between different asset management firms.
Another issue in reporting net returns is that a presented net-return might not be achieved by all clients due to differences in characteristics (volume) or simply bargaining power.
Brokerage Commission Costs are usually added to the purchase cost and subtracted from sales proceeds for both gross- and net-of-fee return calculations
Custodial Fees are typically not deducted from either gross or net performance and are treated as a withdrawal. This is justified when the costs are beyond the control of the investment manager.
Management Fees and other charges for advisory services provided by the asset manager are usually charged to the portfolio. These charges are treated as withdrawals in the calculation of 'gross-of-fees returns' (=before deduction of fees charged).  The same withdrawals are excluded in the calculation of a net-of-fees return (=after the deduction of fees charged). Management fees can also be charged outside the portfolio. It is important to include fees charged are in the calculation of net- and gross-of-fees returns. When fees have been paid from outside the fund, they are excluded from calculations when a gross of fees return is required.  They are treated as a contribution to the portfolio when a net of fees return is required.
To avoid distortions and "jumps", fees payed out of the portfolio should be "accrued"  whenever possible.
If fees are calculated as a percentage of average capital invested, the calculation methodology for average captial invested should be specified as detailed as possible.

Transaction Costs

Transaction costs are usually deducted: securities at 'cost prices'.
Often neglected, source of return, quality indicator for operationally efficient investment management.

Exchange Rates

Portfolio base currency, security currency, currency overlays, currency fowards.
Consistency is oftenan issue: consistency not only within portfolio, but also when benchmarks and other entities the portfolio is compared with are involved.
Data source for exchange rates used should always be disclosed.


Portfolio's Return Calculator

Use these calculators to work out your portfolio's returns.

How to figure your portfolio's return


Q: How can individual investors calculate the rate of return on their portfolios if they have deposited or withdrawn money from the account?

A: I'm always intrigued when people do things with their investments they'd never do with their money in normal life.

Would you order a dish from a restaurant menu without knowing the price ahead of time? Would you buy a non-refundable airline ticket without knowing the fare? While there may be some exceptions, the answer will usually be no.

But investors keep buying stocks, bonds and mutual funds and have no idea what they're paying or, more important, getting in return. And they may be paying dearly either with large mutual fund fees or indirectly with lackluster performance.

Worse yet, they might be fixated on their one winning stock while ignoring the five dogs that are killing their portfolio.

Are you one of these people? You are if you don't know how to calculate the return of your portfolio. You'd be surprised how many people don't. The briefly famous Beardstown Ladies investment club thought they were brilliant investors until it was discovered they were not measuring their returns properly (they counted deposits to the account as investment returns).

Many brokers don't help. Few of them bother to provide rates of return for their customers' portfolios. The cynic in me suspects that if many active traders knew what their real returns were, they'd probably quit trading so much. To the credit of major mutual fund companies, most of them do calculate your performance data.

Well, it all gets cleared up right now. I'll show you how to do this yourself, using 2005. To get started, you'll need:

1. The balance of your portfolio on Dec. 31, 2004, available on your statements.
2. The portfolio balance on Dec. 30, 2005.
3. The dates and amounts of any deposits or withdrawals made during the year.
4. Unless you're a math genius, you'll need a financial calculator or Microsoft Excel.

Let's say your portfolio was worth $10,000 on Dec. 31, 2004. During the year, you deposited $1,000 on March 30, withdrew $500 June 30, deposited another $1,000 Sept. 30 and the portfolio ended the year worth $12,000.

Someone who didn't account for the deposits and withdrawals would assume they did well last year. After all, the portfolio gained 20% in value, not including the value of the deposits and withdrawals.

But let's do this correctly. We'll first do the problem assuming you have a Hewlett-Packard 12C financial calculator, a popular calculator handy for all investors. Incidentally, the calculator is celebrating its 25th anniversary. You can read more about it here.

Keep in mind that each number described above is actually a cash flow. We can plot it this way:
Initial cash flow: minus $10,000. We show this as a negative number because it's theoretically money coming out of your pocket to invest.

Cash flow 1: minus $1,000 — again, a negative number because the money is coming out of your pocket.
Cash flow 2: plus $500. This is positive number because the cash is coming into your pocket.
Cash flow 3: minus $1,000. Negative, see above.
Cash flow 4: plus $12,000. This is the money theoretically coming into your pocket from the investment.

The HP 12C makes this easy to calculate. Here are the keystrokes (note the "CHS" key makes the number negative):

Step 1: 10,000 CHS [g] Cf0
Step 2: 1,000 CHS [g] Cfj
Step 3: 500 [g] Cfj
Step 4: 1000 CHS [g] cfj
Step 5: 12000

Now that you've entered everything, all you have to do is hit the [f] IRR key, and the calculator does the rest. The HP12C will show you that the quarterly return on your portfolio is 1.14%. All you have to do is annualize that quarterly return. To do that, divide 1.14 by 100, add 1, take the sum to the fourth power, subtract 1 and then multiply by 100. You then derive an annualized return of 4.639%.

You might be proud of yourself until you realize that last year, the Standard & Poor's 500 index returned 4.9%, says Ibbotson Associates. In other words, you underperformed a basket of stocks that a monkey could have bought and held in an index fund. And that doesn't even include any taxes you may have paid if you sold any of the shares for a capital gain.

What if you don't have an HP 12C? You can do the same thing in Microsoft Excel. Below is what you'd type into the appropriate cells

Cell A1: -10,000
Cell A2: -1,000
Cell A3: 500
Cell A4: -1000
Cell A5: 12,000
Cell A6: =IRR(A1:A5)
Cell A7:=((((A6/100)+1)^4))-1*100

And you get the same answer in cell A7 that you got when using the HP 12C if you format the cells for "number" to four decimal places. Otherwise, Excel will round things off.

If all this seems like too much work, don't give up. Not knowing your portfolio return is like driving on the freeway blindfolded. Another option is to buy a software program that does the calculations for you.

One piece of software I've used that does this quite well is the BetterInvesting Portfolio Manager. This software program allows you to do enter each transaction into a checkbook-like register and it calculates your return with great precision. It's not cheap, but you can learn about the software and download a free trial here.

Matt Krantz is a financial markets reporter at USA TODAY. He answers a different reader question every weekday in his Ask Matt column at money.usatoday.com. To submit a question, e-mail Matt atmkrantz@usatoday.com.

Posted 2/27/2006 12:01 AM ET

http://www.usatoday.com/money/perfi/columnist/krantz/2006-02-27-portfolio-return_x.htm


Calculate your portfolio return here:

Detailed version:   CALCULATE YOUR PORTFOLIO'S RETURN