Join Early Retirement Today
Reply
 
Thread Tools Search this Thread Display Modes
What does SWR really mean? And not?
Old 05-19-2013, 02:54 PM   #1
Give me a museum and I'll fill it. (Picasso)
Give me a forum ...
Midpack's Avatar
 
Join Date: Jan 2008
Location: Chicagoland
Posts: 11,974
What does SWR really mean? And not?

1 There are often posts here confusing Safe Withdrawal Rate with % of Remaining Portfolio approach - they are not at all one in the same. Where % of remaining portfolio is as it sounds, following the theoretical SWR methodology the % withdrawal is only applied in the first or initial year. After that, withdrawals increase in all subsequent years following inflation. Note the passage in green above.

2 This has been done here many times so with apologies to those who already know what SWR was meant to represent. For others, no need to take issue if you understand the meaning of safe withdrawal rate.

Quote:
Defined: The quantity of money, expressed as a percentage of the initial investment, which can be withdrawn per year for a given quantity of time, including adjustments for inflation, and not lead to portfolio failure; failure being defined as a 95% probability of depletion to zero at any time within the specified period.


Usage: Typically, SWR is utilized as an approximation of the probability that a given portfolio can support a given annual spending component for a required period, with a reasonable confidence. To do this, variables such as the allocation of assets within a model portfolio, the beginning balance, and/or the number of years expected in retirement are varied, a model is applied, and results of these alterations in the variables are observed and compared, in order to optimize for the maximum.


Controversy: Unfortunately, the term "Safe Withdrawal Rate" is necessarily an ambiguous term. This is because initial methods utilized historical data to statically determine what would have been safe given the actual results that past portfolios would have generated with the variables given. The next logical step, of course, was to use that information to predict future SWRs. Either use is technically correct, but one should always be sure to be clear whether the use is in reference to past or projected SWRs, so that unnecessary argument can be prevented.

One scenario backtested in the Trinity study suggests that a retiree with a suitably allocated $1 million portfolio could withdraw $40,000 the first year, give herself a cost-of-living adjustment every year afterwards, and have a 98% chance of the portfolio lasting at least 30 years.

Taken literally, such a plan has been criticized as unrealistic. Even if the tests showed that the plan had a 98% success rate over all past time periods, would a prudent person blindly go on steadily increasing withdrawals in a prolonged bear market? It also leads to apparent absurdities. Say that retirees A and B have saved $1 million in 2008, and the market crash reduces their portfolios to $800,000 in 2009. A, however, retires in 2008 while B waits until 2009. The Trinity study bases withdrawals the dollar value of the portfolio at the start of retirement. The value fluctuates with the vagaries of the stock market. Thus, even though their situations are almost identical, in the Trinity scenario, retiree A, by virtue of having retired in 2008, is allowed to withdraw $40,000 plus COLA in 2009; while retiree B, despite being in an almost identical situation, would be allowed only $32,000.

The authors of the paper, however, did not mean for their scenarios to be applied rigidly or uncritically. The article makes this very important statement:
The word planning is emphasized because of the great uncertainties in the stock and bond markets. Mid-course corrections likely will be required, with the actual dollar amounts withdrawn adjusted downward or upward relative to the plan. The investor needs to keep in mind that selection of a withdrawal rate is not a matter of contract but rather a matter of planning.
Nisiprius requested clarification from Professor Philip L. Cooley, senior author of the Trinity study:
What the "4% SWR" means is not that you can treat a portfolio as if it were a guaranteed annuity. I think all the [Trinity] authors meant is that if it is late 2008 and your stocks halve in value, you don't need to halve your spending instantly. It's OK to cross your fingers and continue spending according to the 4%-then-COLAed plan, even though it means dipping into capital, and it's OK to go on doing that for a while.
Professor Cooley's response:
You have hit the nail on the head! I've tried to explain that thought to journalists but they don't seem to get it. You've got it. Stay flexible my friend!, which is the advice we should give to retirees.
Safe Withdrawal Rates - Bogleheads
__________________

__________________
No one agrees with other people's opinions; they merely agree with their own opinions -- expressed by somebody else. Sydney Tremayne
Retired Jun 2011 at age 57

Target AA: 60% equity funds / 35% bond funds / 5% cash
Target WR: Approx 2.5% Approx 20% SI (secure income, SS only)
Midpack is offline   Reply With Quote
Join the #1 Early Retirement and Financial Independence Forum Today - It's Totally Free!

Are you planning to be financially independent as early as possible so you can live life on your own terms? Discuss successful investing strategies, asset allocation models, tax strategies and other related topics in our online forum community. Our members range from young folks just starting their journey to financial independence, military retirees and even multimillionaires. No matter where you fit in you'll find that Early-Retirement.org is a great community to join. Best of all it's totally FREE!

You are currently viewing our boards as a guest so you have limited access to our community. Please take the time to register and you will gain a lot of great new features including; the ability to participate in discussions, network with our members, see fewer ads, upload photographs, create a retirement blog, send private messages and so much, much more!

Old 05-19-2013, 03:05 PM   #2
Give me a museum and I'll fill it. (Picasso)
Give me a forum ...
 
Join Date: Jun 2005
Posts: 8,619
I just call it the "sustained withdrawal rate". It's never safe.
__________________

__________________
LOL! is offline   Reply With Quote
Old 05-19-2013, 04:07 PM   #3
Give me a museum and I'll fill it. (Picasso)
Give me a forum ...
 
Join Date: Sep 2005
Location: Northern IL
Posts: 18,281
To address one of the comments, I've been thinking we should adopt the term "HSWR" when we reference a FIRECALC 'SWR' to emphasize the 'historical' aspect w/o having to add that caveat so many times.

Just quickly, as I'm just taking a short break from yard work - the 'absurdity' of the retirees with $1M in 2008, retiring in 2008 and 2009 is interesting. Better stated than the way the FIRECALC intro compares the three retirees, IMO. But that just seems like the limitations/realities of trying to plan for 'worst case' - most of the time you won't be in the 'worst case' situation, and you really could have spent more (likely the case with the 2009 retiree).

But what is the answer? I don't feel real comfortable trying to estimate the 'value' of the market at any point in time (in other than a very general way, and adjusting only slightly). Should the 2008 retiree drop to $32,000? Should the 2009 retiree look at this as just a short dip from 2008 and carry on with $40,000 on his recent $1M?

This will be clearer in 2039

-ERD50
__________________
ERD50 is offline   Reply With Quote
Old 05-19-2013, 04:54 PM   #4
Administrator
W2R's Avatar
 
Join Date: Jan 2007
Location: New Orleans
Posts: 38,890
Quote:
Originally Posted by ERD50 View Post
To address one of the comments, I've been thinking we should adopt the term "HSWR" when we reference a FIRECALC 'SWR' to emphasize the 'historical' aspect w/o having to add that caveat so many times.

Just quickly, as I'm just taking a short break from yard work - the 'absurdity' of the retirees with $1M in 2008, retiring in 2008 and 2009 is interesting. Better stated than the way the FIRECALC intro compares the three retirees, IMO. But that just seems like the limitations/realities of trying to plan for 'worst case' - most of the time you won't be in the 'worst case' situation, and you really could have spent more (likely the case with the 2009 retiree).

But what is the answer? I don't feel real comfortable trying to estimate the 'value' of the market at any point in time (in other than a very general way, and adjusting only slightly). Should the 2008 retiree drop to $32,000? Should the 2009 retiree look at this as just a short dip from 2008 and carry on with $40,000 on his recent $1M?

This will be clearer in 2039

-ERD50
I retired in the fall of 2009, and I am pretty sure I could safely spend more than I have been spending.

My portfolio's low during the 2008-2009 collapse occurred on March 9th, 2009. Sometimes I when I am thinking of spending more, I compute my annual withdrawal amount as a percentage of my portfolio's value on that date, just out of curiousity.

That helps in keeping things sane and grounded.
__________________
Already we are boldly launched upon the deep; but soon we shall be lost in its unshored, harbourless immensities.

- - H. Melville, 1851
W2R is offline   Reply With Quote
Old 05-19-2013, 05:19 PM   #5
Recycles dryer sheets
 
Join Date: Apr 2007
Posts: 354
I don't know why, but in my mind I usually convert the "S" in SWR to "steady." And in my mind, that means no more than 4% of whatever the starting balance was, and in down years most likely no more than 4% of whatever the current balance is. That just feels like it builds a little more security (another good S word) into the plan. If I were to go part time at work, or have my hours cut, I'd look closely at the budget for places to cut back, or if there were absolutely no places to cut I'd take on some part-time . I would do the same if I were living off investments and there was a market downturn. Nothing really is safe, because you can't predict the future, but you can make it safer by being prudent and not sticking to any arbitrary plan just because 4% has been judged to be some kind of magical number.

Personally I'm figuring that a 2-3% target is about right and will give me plenty of wiggle room in all market conditions.
__________________
lhamo is offline   Reply With Quote
Old 05-19-2013, 05:23 PM   #6
Give me a museum and I'll fill it. (Picasso)
Give me a forum ...
 
Join Date: Jul 2006
Posts: 11,018
Maybe we should call it a Smart Withdrawal Plan. Smart enough to be sustainable indefinitely under most conditions, but adjustable based on the evidence, should the need arise.
__________________
Meadbh is offline   Reply With Quote
Old 05-19-2013, 06:33 PM   #7
Full time employment: Posting here.
dtbach's Avatar
 
Join Date: Apr 2011
Location: Madison
Posts: 752
I'm pretty sure you could twist yourself into a pretzel trying to figure out the "Absolute" SWR. Einstein probably would throw his hands up in the air.

So just do it one year at a time, adjust up and down as your portfolio goes. No worries.
__________________
Wild Bill shoulda taken more out of his IRA when he could have. . . .
dtbach is offline   Reply With Quote
Old 05-19-2013, 07:00 PM   #8
Give me a museum and I'll fill it. (Picasso)
Give me a forum ...
audreyh1's Avatar
 
Join Date: Jan 2006
Location: Rio Grande Valley
Posts: 16,471
Quote:
Originally Posted by ERD50 View Post
To address one of the comments, I've been thinking we should adopt the term "HSWR" when we reference a FIRECALC 'SWR' to emphasize the 'historical' aspect w/o having to add that caveat so many times.

-ERD50
I was thinking of it as the "up until now safe withdrawal rate", but I like your HSWR! [historically safe]

up until now = so far, so good
__________________
Well, I thought I was retired. But it seems that now I'm working as a travel agent instead!
audreyh1 is offline   Reply With Quote
Old 05-19-2013, 08:11 PM   #9
Thinks s/he gets paid by the post
MooreBonds's Avatar
 
Join Date: Aug 2004
Location: St. Louis
Posts: 2,091
One aspect of the (H)SWR that struck me earlier today is how the dividend yield of the S&P 500 might be relevant to the discussion.

Historically, stocks have yielded higher dividend yields than they do now. Also, it's a known fact that dividends (either reinvested or taken as cash) contribute a significant component of the historical total returns over the years.

Using this as an example:
S&P 500 Dividend Yield - multpl

it shows that for nearly all of the history prior to 1990, the S&P500 dividend yield has been right around or above 4%...which is the magic (H)SWR. Compared to the current yield of below 2%.

I'm curious if anyone is factoring in this statistic (current average dividend yield compared to historical) to their planning? If so, how are you adjusting it?

Personally, I'm hoping to pull the plug with a distribution of 2.75% from my portfolio. My actual current portfolio yield from dividends and small preferred stock holdings are just over 4% yield, but I'll let the extra accumulate as needed, until my distributions drop to 2.6%, then I'll talk myself into splurging a bit more .

Because I'm assuming that the FireCalc returns factor in dividends, and because I don't see equities/corporate earnings growing 2%-3% higher than they used to, I don't see stocks being able to provide total returns (with dividends) near their historical drive. And that's before throwing in the whammy of infinitesimally small interest rate yields.
__________________
Dryer sheets Schmyer sheets
MooreBonds is offline   Reply With Quote
Old 05-19-2013, 08:27 PM   #10
Thinks s/he gets paid by the post
photoguy's Avatar
 
Join Date: Jun 2010
Posts: 2,301
Quote:
Originally Posted by MooreBonds View Post
I'm curious if anyone is factoring in this statistic (current average dividend yield compared to historical) to their planning? If so, how are you adjusting it?
No because dividend yield doesn't drive returns. However, other valuation measures like PE10, PE, etc are (somewhat) predictive and generally suggest that returns going forward are likely to be muted/lower. The high valuations --> lower expected returns is what's driving down what I consider to be a "safe" WR.
__________________
photoguy is offline   Reply With Quote
Old 05-19-2013, 08:42 PM   #11
Thinks s/he gets paid by the post
Rustward's Avatar
 
Join Date: Apr 2006
Posts: 1,572
Quote:
Originally Posted by W2R View Post
I retired in the fall of 2009, and I am pretty sure I could safely spend more than I have been spending.

My portfolio's low during the 2008-2009 collapse occurred on March 9th, 2009. Sometimes I when I am thinking of spending more, I compute my annual withdrawal amount as a percentage of my portfolio's value on that date, just out of curiousity.

That helps in keeping things sane and grounded.
I do similar evaluations.

You have probably answered this in other threads, but what percentage WR do you consider safe, or sustainable, or whatever other tag we put on it?
__________________
Rustward is offline   Reply With Quote
Old 05-19-2013, 08:54 PM   #12
Administrator
W2R's Avatar
 
Join Date: Jan 2007
Location: New Orleans
Posts: 38,890
Quote:
Originally Posted by MooreBonds View Post
it shows that for nearly all of the history prior to 1990, the S&P500 dividend yield has been right around or above 4%...which is the magic (H)SWR. Compared to the current yield of below 2%.

I'm curious if anyone is factoring in this statistic (current average dividend yield compared to historical) to their planning? If so, how are you adjusting it?
I have no idea whether the S&P itself will go up or down, and try not to market time. Likewise, I have no idea whether the S&P dividends will go up or down either, and I try not to act on expectations of a future increase or decrease.

Practically speaking, I pay attention to the dividend yield of my portfolio instead of the S&P dividend yield. Each year I withdraw less than my prior year's dividends and also less than my SWR ("Selected Withdrawal Rate"? ). However, I suppose that if my dividends dropped radically I would still withdraw the same amount, perhaps? I don't know! I guess I would have to live through that to see what I would actually do in a situation like that.
__________________
Already we are boldly launched upon the deep; but soon we shall be lost in its unshored, harbourless immensities.

- - H. Melville, 1851
W2R is offline   Reply With Quote
Old 05-19-2013, 08:57 PM   #13
Administrator
W2R's Avatar
 
Join Date: Jan 2007
Location: New Orleans
Posts: 38,890
Quote:
Originally Posted by Rustward View Post
I do similar evaluations.

You have probably answered this in other threads, but what percentage WR do you consider safe, or sustainable, or whatever other tag we put on it?
I think it depends on the individual's risk tolerance, the length of retirement they expect, and so on.

In my own particular case, I decided some years ago that 3.5% would be reasonable for a 35 year retirement and low risk tolerance. That looks more and more risky as time passes, doesn't it?

Since retirement I have been using 2% instead because there is only one of me, I don't like to travel, I am used to my present lifestyle and level of non-grandeur, and so on. I don't feel all that comfortable spending more and I don't know what I would spend it on. That said, this year my spending might be closer to 2.5% due to a new TV and dental implant. I don't know for sure, yet. Maybe it will end up back at 2% as in prior years of retirement.

2% of my present portfolio is about 3% of my March 9th, 2009 all-time-low portfolio. I guess that is OK with me. I would start to worry if it got too close to 4%, for me. Others have a lot higher risk tolerance, I suspect.
__________________
Already we are boldly launched upon the deep; but soon we shall be lost in its unshored, harbourless immensities.

- - H. Melville, 1851
W2R is offline   Reply With Quote
Old 05-19-2013, 09:12 PM   #14
Thinks s/he gets paid by the post
Katsmeow's Avatar
 
Join Date: Jul 2009
Posts: 3,399
When DH retired 3 years ago I ran Firecalc and saved the results and was doing some reorganizing on my computer and came across them the other day. What is sort of interesting to me is that those results are of only historical interest to me at this time.

What matters to us is how much we have now and what we can withdraw going forward...not so much what Firecalc said 3 years ago.

Our situation is a little more complicated than some as we have high withdrawals until the kids are out of school and completely gone then our projecting spending goes down markedly.

Still, I suspect that even when we are withdrawing a more even amount I will continue to run retirement planners periodically and would be more inclined to go bay the situation at that time rather than looking at what the planner originally said.
__________________
Katsmeow is offline   Reply With Quote
Old 05-19-2013, 09:32 PM   #15
Thinks s/he gets paid by the post
Ready's Avatar
 
Join Date: Mar 2013
Location: Southern California
Posts: 1,823
I've spent a lot of time thinking about withdrawal rates, especially over the past two weeks since I left my job. I know I can live on 2% if I choose to, but I'm not sure how excited I am about doing that. I'm starting to pay a lot more attention to the cost of basics, like gas and food, than I used to.

However, I have to keep reminding myself that bonds won't be at these ridiculously low rates indefinitely, and I'm planning for a 40 year horizon. We really have no idea what life will look like over the next 40 years, but it seems more likely that it won't resemble anything like life today. The biggest concern is watching how the overall market performs in the first decade or so of retirement, since those years can have the greatest overall impact on the remaining years. Ideally I would have retired at the bottom of the market, so I could hopefully predict a long rise before the next crash. It's hard to know where we are now, so the only thing we know is that we really can't predict the future with any certainty.

Basing your withdrawals on the current balance each year, rather than blindly withdrawing a fixed amount each year, seems like the only logical way to go. That's my plan (for now).
__________________
Ready is offline   Reply With Quote
Old 05-20-2013, 08:19 AM   #16
Thinks s/he gets paid by the post
nun's Avatar
 
Join Date: Feb 2006
Posts: 4,836
It's good to be having this discussion here, but the bigger issue is whether the general retiree with an IRA understands all the assumptions of SWR. IMHO no WR that relies on historical data is safe because it has no connection to the current (or future) performance of your portfolio. I'm far happier with WRs that take a constant percentage of the portfolio or are in some other way connected to the actual annual return of the portfolio and of course your need for income.

The 4% "SWR" is a short hand that has become dogma and it's caveats are often glossed over or ignored. The possibility of mid-retirement income adjustments must be included and isn't often enough.
__________________
“So we beat on, boats against the current, borne back ceaselessly into the past.”

Current AA: 65% Equity Funds / 20% Bonds / 7% Stable Value /3% Cash / 5% TIAA Traditional
Retired Mar 2014 at age 52, target WR: 0.0%,
Income from pension and rent
nun is offline   Reply With Quote
Old 05-20-2013, 08:41 AM   #17
Thinks s/he gets paid by the post
nun's Avatar
 
Join Date: Feb 2006
Posts: 4,836
Quote:
I do similar evaluations.

You have probably answered this in other threads, but what percentage WR do you consider safe, or sustainable, or whatever other tag we put on it?
I'd consider a PWR (Prudent Withdrawal Rate) to be something less than or equal to the actual return of your portfolio minus inflation. Of course you'll be in trouble in down years and will have to spend your cash and convince yourself that cash shouldn't be include in the value of your portfolio.
__________________
“So we beat on, boats against the current, borne back ceaselessly into the past.”

Current AA: 65% Equity Funds / 20% Bonds / 7% Stable Value /3% Cash / 5% TIAA Traditional
Retired Mar 2014 at age 52, target WR: 0.0%,
Income from pension and rent
nun is offline   Reply With Quote
Old 05-20-2013, 09:03 AM   #18
Give me a museum and I'll fill it. (Picasso)
Give me a forum ...
Midpack's Avatar
 
Join Date: Jan 2008
Location: Chicagoland
Posts: 11,974
Quote:
Originally Posted by dtbach View Post
I'm pretty sure you could twist yourself into a pretzel trying to figure out the "Absolute" SWR. Einstein probably would throw his hands up in the air.

So just do it one year at a time, adjust up and down as your portfolio goes. No worries.
It's funny reading some of the posts how we/they try to twist the originators conclusions to mean something other than what they plainly said - citing concerns the originators never claimed! You can see it here and many other places, year in and year out, despite what the originators said.

There's no doubt that many have (and will) continue to misinterpret the meaning, but a 4% withdrawal rate was indeed 95% safe from 1871 through 2011 (extended per FIRECALC), a matter of simple statistics that almost anyone can verify for themselves. And you can easily calculate what was 100% safe or any other probability.

Not only have all the qualified originators (and many but not all readers) gone to some/great lengths to explain the reader can't be guaranteed history will repeat itself, isn't it reasonable to assume everyone knows financial or any other history may not repeat?

And with FIRECALC (if not others), you can also (somewhat crudely) enter your own assumptions as to what future inflation, returns, yields, rates allow you to sleep at night. They're great tools/insights IMO, but still only tools to aid in reaching conclusions.
__________________
No one agrees with other people's opinions; they merely agree with their own opinions -- expressed by somebody else. Sydney Tremayne
Retired Jun 2011 at age 57

Target AA: 60% equity funds / 35% bond funds / 5% cash
Target WR: Approx 2.5% Approx 20% SI (secure income, SS only)
Midpack is offline   Reply With Quote
Old 05-20-2013, 09:16 AM   #19
Give me a museum and I'll fill it. (Picasso)
Give me a forum ...
 
Join Date: Sep 2005
Location: Northern IL
Posts: 18,281
Quote:
Originally Posted by nun View Post
... IMHO no WR that relies on historical data is safe because it has no connection to the current (or future) performance of your portfolio. ...
Well, that is an absolute fact, can't dispute that. Interesting perspective.

Hmmm, I'm wondering how to model this, to get an idea how your spending would have been adjusted year-to-year historically, just as a reference point. IIRC, some people have suggested 'tricking' FIRECALC by changing the portfolio fees from 0.18% to (say) 3.18% to represent a constant 3% portfolio draw. Maybe I'll play with that a bit.

I'm guessing that one would suggest building up a cash balance in years where your PWR% (Prudent WR - I like that too!) of portfolio exceeds what you need/want to spend. But that really isn't much different from re-balancing when one is using a HSWR. Difference would be over a long bad market - no adjustment in HSWR, but a PWR would see an adjustment. I guess it's a one-sided SWR plan - you don't increase WR in a good market, but you do reduce WR in an extended bad market. No question about it - that will add safety. The question becomes, at what price? But like so many things, that becomes a personal decision.

Food for thought.

IIRC, haha is taking a similar approach, trying to avoid touching principal, just taking the divs/interest and maybe gains above inflation? Of course, as you get older you can start making some allowances, and plan to spend some % of principal over LE.



Quote:
The 4% "SWR" is a short hand that has become dogma and it's caveats are often glossed over or ignored. The possibility of mid-retirement income adjustments must be included and isn't often enough.
I agree they are often glossed over - heck, 4% HSWR includes 5% failures and that's not good enough for me. While I agree that one needs to include some kind of mid-course corrections, I've not yet been able to pre-define the conditions in hard terms, so they can be applied consistently and unemotionally if the need arises.

-ERD50
__________________
ERD50 is offline   Reply With Quote
Old 05-20-2013, 09:26 AM   #20
Give me a museum and I'll fill it. (Picasso)
Give me a forum ...
Midpack's Avatar
 
Join Date: Jan 2008
Location: Chicagoland
Posts: 11,974
Quote:
Originally Posted by ERD50 View Post
I agree they are often glossed over - heck, 4% HSWR includes 5% failures and that's not good enough for me. While I agree that one needs to include some kind of mid-course corrections, I've not yet been able to pre-define the conditions in hard terms, so they can be applied consistently and unemotionally if the need arises.
Re: hard terms - lots of good info on using 5% of remaining portfolio withdrawal instead of 4% inflation adjusted withdrawal (SWR). Goes a very long way to controlling end of plan residual while still allowing for maximum spending along the way and all but avoiding running out of money. Ideally, I'd think you'd want to use some income smoothing (5 years?) to avoid more radical fluctuations in withdrawals from year to year. I might start with % RP and go to SWR at a later age...YMMV

And here's something in-between that attempts to address "hard terms." A Variation on Remaining Portfolio Withdrawals - GRPWM
__________________

__________________
No one agrees with other people's opinions; they merely agree with their own opinions -- expressed by somebody else. Sydney Tremayne
Retired Jun 2011 at age 57

Target AA: 60% equity funds / 35% bond funds / 5% cash
Target WR: Approx 2.5% Approx 20% SI (secure income, SS only)
Midpack is offline   Reply With Quote
Reply


Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are Off
Refbacks are Off


 

 
All times are GMT -6. The time now is 06:20 AM.
 
Powered by vBulletin® Version 3.8.8 Beta 1
Copyright ©2000 - 2017, vBulletin Solutions, Inc.